I have a 92 Park Ave. that did the same thing. It turned out to be the crank sensor. The cam sensor can cause the same problem. Get a diagnostic check and that should tell you what the problem is. I found that many repair shops do not have the tools to fix it, only a Buick dealer. A special gear puller is needed. You might ask a repair shop if they can fix it before you spend the money on their diagnostic check.
Replace resistors on Instrument cluster circuit board. $1.00 @ Radioshack and about an hour of your time...
just push the hour button and minute buttons only. No other buttons need be pushe
Make sure battery cables are tight and clean especially ground at engine
Turn off any music. press the hour or minute button along with the down arrow on tune and the time should change. Possibly it is the up arrow on tune. Hope this works.
Check the gas cap there is a possibility that the vent is clogged and causing a vapor lock.
It is on the driver side under the washer fluid container. You have to remove the cross support bar and the washer fliud conainer and the airfilter box. It takes about a half hour to remove and replace. All bolts are metric.
The Buick Circus Hour - 1952 1-1 was released on: USA: 7 October 1952
The Fuel pump itself is $112 and you will have to by the strainer/filter(which goes on the end of it) for $9.99. I did mine myself so I cant help with the labor....it was a 2 hour job.
Dirty fuel filter. Get it changed.
Front drivers side underneath the windshield washer fluid reservoir. You'll have to remove the engine brace, reservoir, and the two relays behind it to get access to it. The first time it took me just over an hour to replace, so make sure you get a premium battery.
The cast of The Buick Circus Hour - 1952 includes: Milton Berle as himself Ben Blue as himself Dippy Diers Milton Frome as Ringmaster Frank Gallop as himself Bert Lahr as himself John Raitt as Bill Sothern
Most repair shops have set prices to repair anything. You should be able to ask them ahead of time to get that price. The belt typically runs about $50. That plus the labor time would give you the answer. At $100 per hour rate and about 1/2 hour to replace it, I would guess the cost would be around $100.