To be clear, my opinion on the matter is that the Islamic innovation in Arabia will not occur wherein a surviving Kingdom of India under the dynasty of Menander remains. Matters would be changed immensely in this scenario due to a divergent Arsacid confederacy, likely no Sassanid revolt and a differentiated Roman Empire and Yuezhi-Scythian invasion trend. As such, situations in Arabia are changed mildly, but with mild changes comes significant divergences. Arab conquests of the region however are nevertheless plausible, it is not far fetched in the slightest to imagine an Arab conquest of Iran in a scenario without Islam. However, to the point of the Indian kingdom.
First, we must get our terms correct. The Indo-Greek kingdom, was referred to, as I understand and from coinage, as the 'Kingdom of India' or the Kingdom of the Indus. This is divergent from the Kingdom of Bactria to its northwest in Central Asia. This Indian kingdom was referred to as such due to its situated position along the Indus river. It was however divided into seemingly two separate realms that were roughly united. Namely, the Kingdom of Arachosia and India. Arachosia being the areas east of Drangiana. Arachosia as a unit, would have included much of Drangiana, Paropamisade along the east of the Arius river and also Gedrosia, that being Baluchistan. India, the main political unit, would have included from Gandhara southward to the end of the Indus river into the ocean. This Indian section was the most important of the two and was the crown jewel of the monarchs of the respective regions.
I am not sure that the poster had a POD in mind, I assume it would be between 145-120 BCE, the critical three decades of the Indian kingdom's period.
Menander I (155-130 BCE) was the ultimate Indian kingdom of the Greeks in the region. His reign began during the reign of similarly fantastic kings, such as Mithridates I (171-132 BCE) or his formal name Arsaces V and Eucratides I (171-145 BCE) of the Bactrian kingdom. Menander I was an energetic and phenomenal king, whose skill in battle was matched and exceeded by his ability to rule. During his reign, he was opposed on either side by enemies, namely in the northwest by Eucratides I of Bactria who in 163 BCE, was made a vassal state of the Arsacids and proceeded to invade India and engage them aggressively on behalf of their overlords and in the southeast by Pushyamitra Shunga (185-149 BCE) of the Shunga empie, a successor of the Magadhi state of the Maurya.
Menander I was in his early rule, preoccupied from 153-149 BCE with a major war with the Shunga. In said war, Menander I was able to defeat the Shunga and pushed deep into the Gangetic plain, capturing Pataliputra and subjugating the region and in theory, the Shunga. However, Eucratides I pushed into Arachosia around the year 149 BCE, forcing Menander I back to the west to stifle the Bactrian incursion. This was seemingly a massive success, as the Bactrians were defeated soundly and fled by the year 148 BCE. Menander I then seems to have extended his influence across the Gujarat and other areas. His coinage becomes predominant across northern South Asia, implying a general Indian hegemony over South Asia and dominance of his realm over the rival Shunga. In 145 BCE, the first rumblings of trouble occurred. Scythian nomads, pushed south into Bactria Eucratides I was defeated decisively in 145-144 BCE and seemingly slew in the conflict. His realm was taken in a tide by the Scythians who divided up Bactria among themselves and pushed both west, east and south. North of them, was the Yuezhi, who were more slowly crossing the Kashmir region and acting as possible overlords or as partners with the Scythian tribes that conquered the Bactrians. According to Chinese sources, the Scythians decimated the Bactrians and subjugated them and then challenged in battle the Arsacids, or the Anxi.
Menander I seems to have had problems with this new situation, for in between the years 142-139 BCE, a certain Zoilos I rose to power in Arachosia as a rebel against Menander I and was possibly sponsored by the Scythians or representative of refugee Greeks from Bactria capturing the state in Arachosia and acting as enemies of India and of the Scythians, in that case, sponsored by the Arsadcid king, Mithridates I. Menander I was unable to resolve the issue with Zoilos I and perished around 130 BCE leaving the throne to a young Strabo I.
Strabo I (130-109 BCE) was a boy upon his ascent seemingly, as such he inherited a massive sprawling domain covering the largest population in the world aside fro the Han Dynasty. It was too massive for the child to operate and without the skill of Menander, the state began to falter. Fractions occurred immediately. Shunga resurgence resumed under Vasumitra Shunga (131-124 BCE) who recaptured most of the Gangetic Plain from the Indian kingdom and defeated the Indian state along the Indus, setting their border at the eastern bend of the Indus. In the west and south, the Indian state continued to fracture, Zoilos I remained the ruler of Gedorsia and western Arachosia, but a second Greek took rebellion by the name of Lycias. Lycias would capture the region of eastern Arachosia and southern Ariana for himself and challenged Zoilos I and Strabo I for supremacy. Strabo I was ruling in a precarious situation as his state was limited to the Indus Valley and was pressed on all sides by the Scythians to the northwest, the rebel Greek states to the west and the Shunga to the east.
While India was declining, the Arsacid empire, the preeminent power in the region at the time was fresh off massive conquests. Mithridates I had thrust his people into a position of ultimate power by defeating the Seleucids in Mesopotamia and subjugating Bactria. The Arsacids had plans for an invasion of Syria, Anatolia, Egypt and so forth. The dream then, may have been the recreation of Alexander's empire, certainly. The Arsacids had proven their mettle by destroying all near them and creating a new hegemony. Yet, the Arsacids wherein 133 BCE, faced with a new threat from the east.
In the year 174-162 BCE, wars between the Xiongnu and the renowned Yuezhi state led to the flight of the Yuezhi from their home in eastern Tocharia and the Gansu in 161 BCE. These Yuezhi supposedly, as per the opinion of many scholars, possessed as sort of enormous renown across the steppe region as power lords and prestigious warriors/merchants. Their names may have been mentioned in the texts of Indian epics and their name according to Han records, sent the Scythians into flight just at their mention. Han officials were dumbfounded whence they learned of the defeat of the Yuezhi by the Xiongnu, so perplexed were they that the Han submitted to tribute to the Xiongnu due to recognition that the Xiongnu must be unbeatable to have defeated the Yuezhi, who to them were the greatest of the barbarians in war and wealth.
The idea, is that whence the Yuezhi appeared in Western Asia after passing the Kashmir range, bypassing the Indian kingdom, which had lost the Kashmirs to the Scythians some decades earlier, the Arsacids changed their course. Hearing of the arrival of such a prestigious foe, Mithridates I called off his invasion of Syria and moved east. There he died of old age, luckily, the Yuezhi were not yet interested in the Arsacisds and instead were ranging in northern Bactria. In the reign of young Phraates II or formally Arsaces VI (132-127 BCE), the Arsacids defeated a resurgent Selecuid invasion of Mesopotamia in 129 BCE, and with said victory, Phraates II, now perhaps 19, made a call to mimic the greatness of his father and to defeat the renowned Yuezhi and restore the Bactrian vassal.
Phraates II pushed east through his northern lands and into the steppes north of Parthia, where the Yuezhi were ranging. There, the Arsacids, were soundly defeated and the young king was slain by the Yuezhi, who decisively broke the Arsacid army into pieces. Artabanus I, the uncle of Phraates II and the brother of Mithridates I ascended to the throne as Arsaces VII (127-124 BCE) and vowed to avenge his nephew. The Yuezhi for their part, alongside a horde of Scythian subordinates, invaded the Arsacid realm. Yuezhi forces attacked the ceremonial burial grounds of the Arsacid kings and defaced the burials, destroying the bodies and tombs and then burning the city, then afterwards, the Yuezhi froced their way southward capturing more and more land, annexing all of Parthia and pushing into Media before returning to Parthia in 125 BCE. They were followed by Artabanus I who engaged them in battle and as his nephew before him, was slain in battle and the Arsacids were defeated and totally routed by the Yuezhi.
As a result, the Arsacid royalty abandoned their capitol city of Ectbatana and fled into Mesopotamia, while the Yuezhi raided across Media, gathering loot and tribute from the Arsacids and the Arsacid vassals across the region which suffered under the Yuezhi invasion. This was all completed by 123 BCE, a prior Arsacid hegemony was replaced by a Scytho-Yuezho dominion across the region and the Indian kingdom of Strabo I, was barely able to stand on its two feet. This is what doomed the Indian kingdom.
Following the destruction of the Arsacid power east of the Zagros, the Yuezhi resumed a relatively humble dominion over Bactria, Parthia, Sogdia and Ferghana, facing more their enemies to the east, especially the Wusun and the Xiongnu. To the south of the Yuezhi, Scythian warlords jostled for control. Strabo I perished in 109 BCE, in his death, he left a kingdom descending into shambles. Antialcidas had in 115 BCE, usurped the authority of Strabo I in the north, taking control as a local warlord in Taxila, while Strabo I ruled the southern section of the Indus and the eastern parts of the Indus, losing all of his western and northwestern parts between 115-112 BCE.
Lysias who had possibly defeated and destroyed Zoilos I in 121-119 BCE, was in turn conquered in 110 BCE by a Scythian horde, which asserted rule over Arachosia, Drangiana and Gedrosia. In India, the situation worsened even further. For after the death of Strabo I, his succession was that of four different pretenders. Antialcidas from Taxila, Heliokles from Peshawar and western Gandhara (the Scythian vassal), Polyxenos ruling the eastern Punjab (possibly a Shunga vassal?) and then the legitimate option, Demetrius III ruling the southern Indus valley. All of these claimants would battle for supremacy with the Scythain claimant gaining predominance, conquering most of the Punjab and subjugating Demetrius III.
However, this hegemony was more or less a Scythian induced hegemony, not a legitimate revival of Greek power in India. The Scythian warlord, Maues (98-57 BCE) would enforce Scythian hegemony over the fracturing (once again) Indian kingdom, conquering or vasalizing the entirety of it before invading the Shunga, defeating them and pushing as far east as Pataliputra, instigating a widespread Scythian surge into South Asia. Greek remnant states acted as vassals and local rulers in the Indus until the Gupta period thus.
Considering these facts, we should discuss how to fix the situation,as the reign of Strabo I is the most important thing to remedy here.