83' won't run warm!?

I have a problem with my 83' 12a rx7. The car starts up as well as could be expected for its current condition. It idles just fine and I can drive it a block to the gas station without any problems. If I try to take it over about 45mph It starts cutting out, almost like it is running out of gas. I can solve the problem for a minute or two. I let off the gas for 10 secs. Then downshift and continue driving. Once it starts though I know I only have a couple mins. before it will die on me. When it stalls, I will push in the clutch to try to fix it the way I just mentioned above. The rpms will slowly wind down and it will cut out. If I start it again right away I can normally get about 50 feet without it cutting out. If I wait for the engine to cool it starts and drives (under 45) like nothing ever happened. I found a small leak in the fuel lines under the hood but replaced the lines and it helped but not much. Any idea what to check next.