351 mod 400 trouble

The motor is about 4 years old, in the past had some trouble.
The first big issue was the distributor gear breaking of. after i fixed that, i still had the issue. car would run fine for 20 minutes but after it had warmed up, she would die. doing some vacuume checks, found out that i had a warped head, so i sent it off to get milled. that still didnt fix the problem. that was only a precursor. it turned out, i jumped a link on my timing chain. had to get gears and chain replaced at a price. that fixed my car for about a year, except for having to check and adjust the timing. I thought this was the norm, but i guess its not. recently, we had a lot of rain, and my thunder chicken doesn't run the greatest in the rain. I drove the car to work, and everything went smoothly. 8 hours later, the car starts up fine. i gas it to kick the carburator down, and it doggs out. sounds like its going to stall. the rpm doesn't even change. even took the air cleaner off and it did the same thing so it isn't the choke... you hear a nice steady idle, press on the gas and it sounds like its going to stall. it gets silent with your foot tapping the gass. after about 45 seconds of letting it run, it dies. checked the timing, had to adjust it again. checked all the plugs, plug wires, coil, distributor cap and rotor, vacuume lines........ my father thinks its the timing chain again, but he insisted i get a second, third, fourth opinion jsut to be sure. A timing chain is something i can't do that easily myself.. thanks guys!
Sean

Is it an aftermarket cam or the stock cam? If its a performance grind, then stock timing and carburetion won't cut it.

It sounds to me like its time for a good old fashioned carb rebuild. Everything you describe is exactly a symptom of a faulty carb; sunken float, bad needle/seat, gunk in a jet, stuck step-up piston, faulty accelerator pump, leaking gasket... just rebuild it.

before i found out the timing chain skipped a tooth, i rebuilt the carb. this was about a year and a half ago. are you sure it could be the carb? like i said, it started up fine in the morning, i drove about 5 miles to work. there was a lot of water on the road. after work, the car started right up, like normal. i went to kick it down, and it wanted to die...