All of Saladin's sons are too young to rule in 1177, so Saladin's domains will either fall to his brother Al-Adil or is split up among various stakeholders. At this time, it's probably small enough that one man could hold onto it.
However, you likely do not get the greater state Saladin assembled after 1177. There won't be one Muslim state that controls not only Egypt and Damascus, but also significant parts of Anatolia, Mesopotamia, Aleppo or Mosul. All the latter parts will likely remain separate. The Ayyubids also likely lose control of Yemen, and may face revolts elsewhere.
So at this point, while the general Crusader strategic situation hasn't improved from what it was historically, it also hasn't deteriorated. The Muslim powers around them remain divided and unlikely to move in to destroy it utterly like what Saladin did before the Third Crusade arrived.
Which means the Crusader states are still intact with some depth (controlling not only a fortified Jerusalem, but also the fortress beyond the Jordan which offered some protection and cut off Muslim Syria from Muslim Egypt).
With Saladin dead, what are the chances the Muslims can mount a successful attack anytime in the next hundred years to push them to the coasts? Probably not much. With another hundred years of consolidating control and bringing in more settlers, the internal Crusader society will be stronger. They add up after a while. Which means - if we keep the Mongol events intact - that when the Mongols reach the Middle East, you have a much better Chrisitan position. Which means either the Crusader states are destroyed by the Mongols, or they cooperate like the Armenians did to survive, and the Mongols invade Egypt.
Eventually when the Mongol domains collapse, you have a much improved position for the Crusader states, and an opportunity for them to seize enough land to cement their position (let's say Damascus and Aleppo which creates a strong position where the only threats can come from the north (Anatolian Turks) or south (Egypt). Combined with other significant Christian powers in Anatolia (Byzantines, Armenians, and Georgians), we are looking at a viable state that can last a long time.
Is this the most likely outcome? Maybe not. But it's at least a possibility, even a strong one. Of course, there is always the potential for another Saladin figure to come along in the next hundred years - but such decisive figures usually don't repeat so soon, or that the Mongols simply destroy the Crusaders. But if they do hold out, you have another 200 years or so of Crusader control over Palestine and much of Syria with much weaker and divided Muslim states. You have a Byzantine Emprire that never suffered through the 1204 Crusade, and likely decent powers with Armenia and Georgia to keep the Turks off their back. That's not a bad position to be in, and much better than what the 1300s and 1400s were like for the Christian states IOTL.