car runs for short distance and then quits running on 1991 Buick Skylark

the car will run for about 5-10 min. and then shut off... then has trouble restarting but sometimes if you just let it sit for a little bit it will restart and do it all over again... we just replaced the fuel pump and filter.

check ignition module, crank sensor & cam shaft sensor
4 more answers
Several problems can cause this like choke problem, bad fuel pump or clogged fuel filter checkout this article
Check for a bad relay, coil, or ignitor
check pcm/ebtm
IN WV ALSO! I have a 1993 Buick Century 3.3 V6 after driving 5 miles or so above 25mph and then slowing down to come to a stop would sound like a standard 'bucking' when the clutch isn't pushed in when slowing down, and when I came to a full stop it would stall; would always restart but die when taken out of park and after 10 or 15 minutes rest would be driveable. New fuel pump (sending unit & filter) and full tuneup (plugs and wires); everything else checked out ok, but after 4 mechanics were stumped and nearly $500 of scopes and scans it is the torque converter clutch solenoid; they unhooked it and it runs fine. My car does not have overdrive...I don't know if an overdrive model would run with it unhooked completely. Another test was it also would not stall if I put it in neutral as I was slowing down to stop. I have heard faithfully changing the transmission fluid and filter more often than recommended helps to prevent this, but in the end it needs a torque converter clutch solenoid if it is to the point of no return, i.e. more than a sticky occasional problem.