The Third Crusade had many things going against it. There was the refusal to adopt the local Arabian horses, which could carry a fully armed knight, albeit with a slower top speed than the European mounts. The crusaders were only going to spend a few years and then wander back home, leaving behind just the Kingdom of Jerusalem to fend for itself (I think its the only one left anyways...). They were unfamiliar with the terrain. And most of them were really bad tacticians, or at least let hatred override tactical sense. They were outnumbered almost as badly as the Mongols were when they attacked proto-Russia, except the Mongols had tactical sense and the Catholics kept falling for fake retreats against the Mongols. The crusaders cannot expect to enjoy that advantage to offset their numerical problems.
But let's say the Third Crusade succeeds in recapturing all of Jerusalem and stamp out any guerilla resistance. Let's also say Richard the Lionhearted of England makes a limited offensive into the Levenant and advances all the way to the cities of the Tigris river, beating a field army three times the size of his own.
OK, now what happens? The Tigris area is outside of what the crusaders were intending to keep anyways. Sure the Muslim field armies were defeated and many of them dead, but they can make another army. Does Jerusalem just fall in a decade after the crusaders leave? Did the crusaders bring people to settle the place? The area gets little rain, so the kingdom would be poor (yes the Arabs were on a large piece of desert, but they had Egypt too so they weren't poor), preventing them from recurring mercenaries to defend themselves.
But let's say the Third Crusade succeeds in recapturing all of Jerusalem and stamp out any guerilla resistance. Let's also say Richard the Lionhearted of England makes a limited offensive into the Levenant and advances all the way to the cities of the Tigris river, beating a field army three times the size of his own.
OK, now what happens? The Tigris area is outside of what the crusaders were intending to keep anyways. Sure the Muslim field armies were defeated and many of them dead, but they can make another army. Does Jerusalem just fall in a decade after the crusaders leave? Did the crusaders bring people to settle the place? The area gets little rain, so the kingdom would be poor (yes the Arabs were on a large piece of desert, but they had Egypt too so they weren't poor), preventing them from recurring mercenaries to defend themselves.