1981 Corvette, what is a fuel tank pressure control valve? I see in the manual where this is listed  as a possible problem but no details are in the manual.

I'm not sure...there may be a terminology issue. The only "pressure relief valve" of the fuel tank that I am aware of is built into the top of the tank itself. It's purpose is to blow off if the tank reaches a dangerous level of pressure.
The only other thing I can think of is the purge valve on the charcoal canister. The fuel tank is a sealed type, but vapors are supposed to be routed to the canister, and then sucked into the engine while running.

What problem are you having that lists this as a possible cause?

My re-occurring loss of fuel issue surface again yesterday. At times when out for a drive, about 25 miles and temps above 70/f when I stop for a short time, say 5 minutes, every once in awhile when I recrank only the fuel in the carb's bowl is used and then she shuts down and I have no fuel to carb.

This might clear it up This Shows the purge valve, could this be a gas cap issue ?

I thought we had already suggested loosening the cap when this occurs, didn't we? Sometimes, the tank may not vent properly thru the vent line to the canister(I've blown MANY spider/bug webs & even rust out of those vent lines in my time), and while drawing fuel from the tank, the pump could be drawing a vacuum in the tank, keeping fuel from going to the front. It's a rare deal, but entirely possible.
As far as raw fuel running out of the "S" hose, the tank would need to be almost completely full for that to happen, since on your car, the fuel has to come out the top side of the tank, unlike the older Sharks, where the fuel came out the bottom of the tank.
Were you having this problem before changing the fuel pump? I gotta ask, even tho I think you prolly replaced the pump because of this problem. It's possible the pump is just not working correctly, and drawing enough suction. The only real way to test that would be to install a pressure gauge on the line to the carb. You could also temporarily put a vacuum gauge on the INLET side of the pump, and crank the engine, to see how much vacuum it is capable of pulling.
My only suggestion is to drive it with the fuel cap loose for now.
One other really off the wall idea is that it is possible the cam lobe on the cam that the fuel pump runs off of is worn, and the pump is just not making a full stoke. This usually makes a noise, but it's not always audible. If yo remove the pump, and the pushrod, take a good look at the end of the pushrod that rides on the cam, up in the engine. There should be NO wear at all on it. I have seen this happen, but not very often. I do know the cams from the '78-mid '80s Chevies had a bad wear problem from not being properly heat treated at the manufacturer....

   I spoke with my mechanic, Dub at Corvette Etc in Charlotte this morning, he did the last work, replacing the fuel pump due to this problem. When he had car then it would crank up okay then so was kinda chasing a problem that wasn't there at that moment. Dub feels may be the pump again, although it has an AC Delco pump on now. He did check the lobe when he swapped pumps and felt it was good.

    Sometimes this loss of fuel happened when I stopped to gas up, so cap was removed and reinstalled and then she just stopped after fuel in carb bowl was used up. So lossening the cap did not change the problem. Yesterday was a 90/f day so only occurrs when it hotter, but not every time so what can work and then not work just to heat?

   As I now going to get a rollback in the morning and get it back to Dub and hopefully still be lacking in getting fuel to carb and maybe he can nail down the problem. Either way I will get a new gas cap just in case.

I have this problem with my '76, kind of.

After sitting for more than 24 hours it takes 7 - 10 seconds of cranking to start.

Checked the carb and replaced the fuel pump, no change.

They did tell me that there is some kind of check valve back by the tank.

I will investigate, replace/fix and let you know.