We are currently looking into this problem and hope to have an official fix soon.
In the meantime, we have received reports from people who have found workarounds for this problem. The following is not guaranteed to work, but it has helped a lot of people.
1. Turn off the Xbox 360.
2. Disconnect everything from the USB-ports on the FRONT of the 360 (if applicable, network adapter on the back USB does not need to be disconnected).
3. Turn on the 360 and connect a controller (wired or wireless). Load a saved game in Jerusalem.
4. Quick travel from Jerusalem to Acre.
5. From Acre, go by horse to Arsuf.
6. Now, the game should work as intended.
Workaround 2:1. Plug in a second controller into the system.
2. Go to the last zone with the horse (The same zone where you fall through the world with the horse and then the 2 Altairs appear)
3. Once you enter the zone, disconnect the second controller.
4. Play normally and the game will save after the mission.