Car stuttering cuuting out under load?

[Asytole]

I have this continuous problem and i'm at a loss guys.My 86 notch 2.3 automatic keps cutting out under load.It starts and idles fine.Itball started this winter during an extreme cold snap.The fuel pump and fuel filter ahjve been replaced,I thought there may have been water or bad gas in the tank,so i pulled it down and emptied it out.The carbuerator was rebuilt twice and i just replaced it with a very good one off of a wreck.It's the 1 barrel computer controled job.Every time i think the problem is solved,it happens again after about a few miles.It feels like it's starving for fuel and when i let off the excellerator it runs fine.Sometimes i acan let it sit for a few moments and will run fine for about 1-5 miles and then the problem starts again.Please help it's my daily commuter for now.Bruce