I had something similar to this happen when I was building an LCD projector, what was going on with me was the thin ribbon cables that go from the LCD screen to the PCB were shorting out/making poor contact. For me it was due to the position of the PCB, but in your case the ribbon cables my be coming unglued from the LCD because of heat or age, or both. This instructable https://www.instructables.com/id/Repair-a-Malfunctioning-LCD/ shows how to fix that.Another thing that could be happening is that the controller board is crapping out on you, open up the projector and see if there are any capacitors hit with the capacitor plague or the like. If it's a really nice projector, then you might be able to find a replacement controller board on eBay, they have quite a few. Otherwise with some searching you might also be able to find a replacement LCD panel. Hope this helps!