I’ve only recently begun studying the crusades, so I am not sure if this is the case but…
I think that 9.11.1565 was the last real push the Ottomans made into Europe, when they were held off at Malta by the Knight’s Hospitaller.
http://op-for.com/2006/09/september_11th_1565.html
As for the Crusades. You are making one fatal flaw in assuming a greater unity amongst crusaders than there really was.
You can look at it sociologically, and it makes more sense than really looking at it as two solid sides. The likelihood of going to war is significantly higher with your close neighbors than foreigners. The reason being that you deal with your neighbors all the time and have property disputes that can boil over and gain support of entire clans.
One of the ways to keep clans from infighting is to raid across the bigger border to invade the mutual foreigners. It was a great way for Rome to unify people under a single banner, as it was a way for various Muslim Sultans and Caliphs to unify people under a single banner. It was a way for nobles to increase their prestige. Whether you are a lowly lord or Duke who gets elevated to become a higher station through your fighting in the crusades, or a King who cannot rise in rank, it behooves you to bring honors to your name and to your title that you can then pass on as part of your estate.
The crusades were often a legitimate excuse to fight wars of conquest for honor, by assaulting the ‘other’. Both religions argued for their own primacy, and conquered many other religions in the process. They just happened to be powerful enough to but heads without a major fluctuation in the ownership of territory. The Christians had taken over Rome, and the Muslims had taken over Persia, essentially.
It costs a lot of money to raise and maintain a standing army, more expensive the further you get from home. It is hard to sit outside a rich city like Constantinople, watching your riches go down the drain, with an army that expects to get paid, and not see the jewel in front of you as an attractive solution to your problems. You can increase your own wealth, while providing some of the spoils to your troops. All the while, there is tension between these armies and the Byzantine rulers because the Byzantines had to help provide for the army crossing its land.
It was because of things like this that the Knights Templar became necessary, because they protected pilgrims and acted as a bank for the European nobles, in their trips to the holy land. Much like the Military Industrial Complex of today, the Chivalric orders developed power in their own right, and a purpose had to be funneled to them. That purpose came from the Crusades.
‘The Crusaders’, didn’t really sack Constantinople. ‘Some Crusaders’, sacked Constantinople. What those religions provided for was a larger scope as to who is ‘us’ and who is ‘them’, in the evolution of our tribal matrix through feudalism on into nationalism and corporatism, which spand beyond ethnic grouping. It’s just the same old tribal behavior on a larger scale.