Car shuts off while driving!?

[tomatinaton]

Hi everyone, I have an 85 gts with an extremely abnormal problem, and Im desperate for help. After driving for a bit I will be accelerating and while on the gas the power will completely cut out for 1 or 2 seconds then jut back in again and cut off again until I ease off the gas. I first noticed this while taking corners but later realized it also happens while accelerating on straightaways. However it only happens while I'm on the gas fairly hard or floored, and If I go get gas the problem disappears for a while, and it seems that the lower the fuel gage reads the more severe the problem gets so for now I've been filling up when the fuel gauge gets down to 3/4 or so. Also it only does it when the car has thoroughly warmed or when driven with a good amount of enthusiasm otherwise the car only has 66,000 miles and the engine runs excellent when its not experiencing this problem. Any help would be appreciated.