There would be no rebellions in the Eastern empire; there were none in OTL, not even after he'd just conquered the place and then marched on in the general direction of India. The rebellions were among the Greeks, and then only because there were false rumours of his death. The premature uprising had ended horribly, and when Alexander really died, you see that the Greeks did nothing until they were absolutely sure that he was
really gone this time. And in Persia? No rebellions upon his death. Wide-spread mourning. The mother of the Emperor he had overthrown
starved herself to death in mourning for Alexander. He was admired in Persia. Which is no surprise, since he was a liberator to most satraps: he lowered taxes and he took a hands-off approach. The only thing he didn't tolerate was corruption and fleecing of the populace. But other than that, the satraps had broad discretion under his reign.
Then there are the supposed invasions. I doubt those would materialise. The real contended would be Chandragupta, who was a cautious and canny ruler. He took the eastern satrapies in OTl because the Diadokhoi were fighting in the West, and Seleukos couldn't do anything about Chandragupta's blatant land-grab. In the ATL, Alexander
can do something about it. Why would Chandragupta start a war like that? He simply took the easiest road to new gains in OTL. If he does the same in the ATL, that means
not invading Alexander's empire, but instead focusing his attention on the parts of India he hasn't conquered yet. So he'd do what Ashoka did in OTL, but earlier.
Alexander, therefore, is quite secure, and will most certainly undertake a campaign in the West.
After his death:
@Daylight Savings has the right of it. If Alexander lives to be 96 (or even 76, which would be more credible), his reign will be among the longest and most prosperous in recorded history. By then, the simple tax revenue of his many conquests (including his conquest of Arabia, which he was actively preparing, so that was
definitely happening) would have long since earned back the costs of the campaigns to conquer them. Control of all meaningful East-West trade (both overland and oceanic) would have made Alexander's empire
ludicrously wealthy. Literally everybody would be under the distinct impression that the God-Emperor Alexander had brought about the Golden Age. He'd have a 100% approval rating. Unless his heir is the most incompetent moron ever, the dynasty is as secure as any dynasty can ever be.