1992 Buick Regal Stalling, Sputtering, Dying

I have a 1992, Buick Regal Custom, 3.6L, V6.

Recently, the car started stalling and dying while idle at stop signs, lights, or parked. I would have to keep accelerator applied at all times to keep from stalling out. Even more recently, the car began stalling/dying whilst in motion (sometimes at over 45mph), or going up a incline, it would sputter and more often than not stall out. Within the last week or so, after stalling, the car would turn over but die immediately and would not stay on, would have to let sit for 20+ minutes, retry, and then it would work for about 5-10min before stalling out again.

Recently, drove the car to the store (about a 10 minute drive), no problems on the way there, was not idling hard, did not stall, no sputtering, nothing. After going in the store and coming out to leave, the car would not stay turned over, and kept stalling for 20+ minutes.

Important Note: The "Service Engine Soon" light has been off and on for about a year now. I have had these same recent problems in the past when that "Service Engine" light was NOT on, then the light would come on and the car would operate just fine until recently.

Any help with this problem would be greatly appreciated.