1999 Mercury Marquis Motor stalls

Couple months ago my car started stalling at idle or when I stop at a light, or 4 way stop. I try to fire it up an I get a pop or a puff under the hood!Ive always got to apply pressure to the pedal to keep it running. Some times it wont crank ive got to push it off the road then it will fire up no problem. This problem has moments it work s fine for weeks an thanit will happen for aday or tocrappy than works for a week an such. I put a new battery in, starter, had the injectors flushed a 3 part cleaning, flushed the motor, installed new plugs. What know!