Sorry in advance for the long post.. I just need to explain as best as I can..
OK... First off, I loaned my Sammy to my sister a few years ago and just got it back. Well, part of it was in a box. Seems it was runnung fine one day and after a brief stop at the store, it wouldnt start. They had it towed to a shop and the guy tore it down. $90 later, they got a phone call stating that the Distributer was junk and the oil pump was shot. Quote to fix was $700 + what ever else they would find. At that point, I was called and asked if I wanted my Sammy back. I said yes and took a 400 mile drive and towed it back home. (Driveshaft in back seat ). The next day, I took the box of parts and reassembled the motor. Low and behold, it started on the first crank!. Now, 2 weeks later, I pull into the parking lot, return the movie I rented and was leaving, I hit the speed bump with a thud and lost all power and the motor DIED..
I pushed it to a parking spot and began to crank it over. No luck. Thinking it may be the timing belt, I poped the Dist cap and looked to see if it was turning. It was.. I put it all back together and cranked again. No luck. Then, I moved a few hoses and wires and tried again and it started to take. Finally it started and I drove home.  Im beginning to think this is what had happened to the sister.. Anyone have a clue where I should look next?  My idea is possible the auto choke. Right now, I made it full open and it is running GREAT.. Could that be it? I see lots of electrical going to the carb. I have NO CLUE what Im looking at since Ive basically been a Chevy guy all my life.  I originally bought this to tow behind my motorhome. Now it has about 55,000 miles on it.  I really want to restore this back to its original glory, but I would really like it to be dependable.  Sorry about the long post, but I felt I needed to explain as best as I could..   Thanks so much in advance..

I'm going to suspect a loose wire somewhere,  or a dirty connection.   maybe a failing battery cable.

If it does it again, it could be the ignition module in the distributor,
I had one on my Chevy truck that worked fine and then went on
and off when it wanted, changed it out and no more trouble

Wild

I would first take a look at your main power wire coming off the battery. Mine did the same thing head lights worked but engine was dead as a door nail.

Weather permitting, Im taking it across town tomorrow (with my AAA card) and hope I have no issues.  As for the above reply, shouldnt it keep running without the battery? I would think the alternator would keep it going. I could be wrong though.  I know my truck had a dead battery and once I jumped it, it ran fine all the way to the local LEs Schwab for a new battery..  Im going to check ALL electrical connections in the morning. Its been raining for the past few days and I have it parked out of sight, out of mind.  I really want to start driving this again like in the years past. It is such a kick to cruise down the highway in a Sammy.  Its slow, bit it's "cool" to be slow in a Sammy! 
If anyone else has any ideas, Im hoping to hear them.  I plan to keep this baby for years to come!

Well, I took the Sammy for a short drive and no issues.. I still need it to prove itself before I venture out too far from home... Im still open to suggestions...   Thanks!

I would probably start with looking at the the wires going to the coil.  The next time it happens you need to have an extra spark plug and pull a plug wire off and put in the extra plug and see if you are getting spark.  If not it has to be somewhere between the coil and the distributor.  It has to be a bad connection somewhere.

Not alot of electrical stuff on a 87.

GREAT IDEA!   Ill give that a try!   Thanks!

On that note, just pull the coil wire on the distributor and stick it under the
wiper blade arm to see if there is spark. always make sure the spark is going to
ground, I fried an electronic spark unit once on a Toyota by not grounding

Well, I have made it to another week and still no problem with it stalling.  My only concern is rough idle when cold but gets alot better once its warmed up.  Guess it could be time for a carb overhaul?

Well, I have made it to another week and still no problem with it stalling.  My only concern is rough idle when cold but gets alot better once its warmed up.  Guess it could be time for a carb overhaul?

Have you got the warm air pipe fitted from the exhaust manifold?

Yes...  That was one of the first things I checked.. Im going to take a drive up to HAWK Suzuki here in Oregon this week and buy a new cap, rotor, and wires.  Ive replaced the plugs and they were all used up.. ( I think they were original's ) Hopefully, the inexpensive stuff will be the right fix..  I see the carb's are rather pricey! 
Thanks for your suggestion!