Assuming it is a pressure balanced valve (required for awhile now), there is a sliding piston in the valve that adjusts the flow if the pressure varies on one side or the other. This can shut off one supply or the other if there is a 'hiccup' in the system (like someone flushing the toilet) which prevents the water temperature from changing too much. It may be stuck to one side if both input supplies are okay. I'm not familiar with the guts of that valve, so maybe it could be cleaned up, but a new cartridge should fix it if it can't. This piston must be free to move, or it can demonstrate the symptoms you've seen.