When I worked with the local Board of Education, the most common problem was dirty filters. Most projectors have 1 to 3 air filters for the fans that collect dust. You should clean them regularly with a can of compressed air to ensure optimal air flow. Otherwise, without enough air, the project will overheat, and as a safety mechanism to prevent physical damage or fire, turn of.
Most filters can be taken out through slits in the bottom of the frame. Some, however, cannot be taken out, and the easiest way to clean the filters and/or projector itself is simply to take a can of compressed air to it.
Just be careful not to tilt or turn the can of compressed air upside down, as the liquid inside can come out. I don't believe it's safe to touch; I have read that it can cause frostbite.