Is your fuel tank vented? I had this problem on my 63 Valiant. It had a non-vented fuel cap and when I would drive it at speeds, it would fall on its face. 1 day I pulled into the fuel island after spirited driving and when I took the cap off, you could hear the air rush in and the tank make a "donk" sound. When I started it back up, ran great for a little while, then would act up again. Popped the cap and the air would rush in and it was fine again. Car was a 6cyl originally and had a V8 swap. Its been off the road for a while now going to a better V8 and this time I will get a new vented tank and larger fuel lines.

If you tank is vented, the vent may be plugged, or your fuel pump coukd be bad or your fuel lines clogged.