starts, runs, dies, starts and runs again...help

I have a 92 Buick Park Ave. Ultra with 108,000 miles on it. For sometime now it has had the problem of dying on me after it has been idling (I live in Michigan so I let it warm up during the winter.) It always started right back up and would then run fine. Now however it has started dying after it has been running for about 20 mins. (this normally happens when I take my foot off the accelerator) Sometimes it will start right back up and sometimes I have to let it sit for a while. Could someone please give me an idea what could be causing this strange behavior? OH and sometimes it will just cut out and then pick right back up while going down the road...kind of like it was turned off and then turned right back on...Thanks

More than likely, you need to change the crank position sensor (CKPS) ; however, it would not hurt to clean the idle air control (IAC) first. Do you have any codes (CEL's)?