stalling 327

hello all,
I've got a 1962 vette with the 327-250 that Im having some stalling problems with. when I start it up for the first time it runs wonderfully and will continue to do so untill I turn it off for about 20 min. anything less it seems to start and run just fine. anything after about 2 hours.. same thing. Doesnt seem to be just heat related. I had the engine rebuilt about 2000 miles ago but didn't have the carb done at that time.
any ideas where I should start? carb rebuild? also its the orig carter AFB.
Thanks,
-Joe

Do you think you could be getting Vapour lock??

Kinda sounds like a choke problem, thats where I myself would start looking

thanks guys. I wasn't thinking vapor lock just due to the fact that I didnt have these problems before having all that engine work done. could be though Ill look in to it more . anyone ever rebuild a cater afb?
thanks again,
-Joe