I had a similar problem on my Burb for a while. Everything worked great till the truck got fully up to temperature and then it would start dying on me just like you described. Didn't help that it died in the middle of a major intersection when I was taking the wife for a ride for the first time in months. Turned out the carb wasn't bolted down tightly enough. I had rebuilt it and put the nuts back on without lock washers. Over time the nuts worked lose. With the engine cold it would start and run fine. Once it heated up I guess things would losen up and it would suck air in under the carb (massive vacuum leak). After sitting for a while it would start again but start stumbling bad after a little while and would eventually die. I didn't discover the lose carb nuts until I went to remove it to do an internal inspection. I got some lock washers and tightened it back in place and the problem was solved.
You said you rebuilt the carb recently so that got me thinking maybe you have the same problem I did. Won't take but a minute to see if the carb is bolted on tight.
Good luck.
