car stalling please help

1987 cutlass 6 cyclinder (i think) stalling,,,,,,,driving down the highway and the car will just die, no warning at all. the lights stay on inside and outside. when trying to start the car back up it will turn over and sometimes back fire but will not start right away, takes about twenty minutes to start. after getting the car started again it did the same thing again about 5 minutes later. it did this total of three times in fifteen minutes and i have not been driving it since. one more thing, the few days prior to this happening it was taking me a few minutes to get the car started. i would very much appreciate any help or suggestions anyone would have to offer us.
thanks

check all basics

prolly a fuel pump that slowly failed.

I had an 89 Buick with a 3100 engine that did the same thing and was told that it was a sensor in the transmission that would cause this to happen but only when the cooling fan's on the radator came on.
What I did to check this out was when the car died and wouldn't restart I would pull the fuse for the fan, the car would restart every time, I ended up just unplugging the sensor and everything worked fine but I didn't have overdrive