Buick had a real problem with cars starting good and running fine for a while then shutting down or dying only to start almost as soon as you could get the car stopped only to run another 10 miles or less before it did it again. If you look on the internet you will see the net is full of people with this problem. I looked for recall notices and everything else and couldn't isolate the problem. I bought a 1998 Le Sabre with 7500 miles on it in 2007 and between 30,000 and 40,000 miles it started dying when I would drive. It didn't do it all the time and I noticed that it primarily occurred after the engine was hot and mostly in the summer. For some reason it did not happen in the winter. At first the shop though it was the MAP sensor shutting sown the fuel flow so we replaced that. NO luck. The fuel pump pressure measured fine, and they checked everything else they could think of. They ran it for hours and couldn't duplicate the problem. I brought it in when it was hot and had been dying and still no luck. I could tell it was starving for gas, so I eventually told them to change the fuel pump even if it did check out fine when they put it on the gauge. Turns out the old one was having intermittent problems. After changing the pump I have had absolutely no problems with the car and now have about 94,000 miles on it. So If you are having problems with the car dying but then restarting after it sits a minute or two think fuel pump even if it checks out. Good Luck.
Because its a 1988 Buick LeSabre
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If you lights do not dim when turning key, then probably your starter.
replace the cooling system in the car. clogged fuel line. could be stuff in gas tank. when it stops,start taking fuel lines apart!
car stalls backfires hard to start
Turn ignition on for ten minutes. Turn off for five seconds. Turn on for ten more minutes. Off five seconds. Lastime on for ten minutes. Off and START IT! Read a book to pass off the time.
it sounds like your neutral safety switch
Change the oil and filter. Pour in 4.5 qts. Start the engine and run for 2 minutes. Shut it off, wait 15 min and check the level. Fill until it is full. You will then have your answer.
the contact wires under the driver side airbag may be stuck
check igntion coils
fuel pressure injector pulse idle air control motor