Try turning off all automatic functions in FMP12 (like sharing, updating etc) and send the app to the background, i.e. hidden. Then look in your activity monitor, and you'll see that the thing is still eating CPU cycles – in my case about 0.5-1%. It shouldn't do anything, just sit quietly and let the system page its memory out.
Could this be connected to the lousy performance that is oftenly reported for the FMP12?