Kurtis G
There's a number of possible problems. If you don't feel comfortable opening the unit up, then you'll need to call a tech. My guess is that it's getting hot and the pressure switch is turning the unit off. 1st two things to do; 1. Clean both of the coils from the inside out using professional coil cleaner. (Follow the safety precautions! Wear goggles and other protective gear!) 2. Check the capacitor(s). Replace if needed. After that, diagnostics gets too complicated to explain.

gizmoe
You are not clear enough in your question of what part is shutting down. You hear the compressor shut off but the fan continues to run? Or everything shuts off? Since this is a window unit the only type of control other than the thermostat would be a freeze stat that would shut the unit down when ice or frosting occurs. That is why the manual suggested cleaning the filter. Freezing occurs when the filter gets plugged or if the coil itself gets dirty. This would be the indoor coil that is located behind the filter. It could be shutting off the compressor by the thermostat if it is defective or if cold air is recirculating back into the unit like when the front cover is off not allowing the air to be directed away from the inlet (filter area).

repairman
2 possibility..! One condenser outdoor unit too dirty ( needs professional overhaul cleaning ) And another one your compressor overheat. Please check it this 2 damn thing... sure you found the problem soon.