When trying to accelerate while driving on the highway there is no throttle response

Hello. My car has been having a problem for a couple years now. It runs fine around town, but when I'm on the highway for an hour or so, the problem starts. When I press on the gas to speed up, it doesn't do anything. It's like pressing on the gas cuts off the fuel supply. (But it doesn't shut off.) If I let up off the gas a little, it kicks in again. If I pull off to the side of the road and put it in park, the engine runs fine. If I press on the gas, the engine revs up just fine. But if I start driving again, I get the same problem again. If I shut off the engine for 10-15 minutes, it starts up and will run fine again for a while. But then the problem soon starts up again. It's as if something gets hot, which affects the car's ability to accelerate; and when you let it cool down, it runs fine until it gets hot again. But again, this never happens just driving around town - even if I'm running around for an hour or so. Sometimes a two hour drive down the highway will require that I pull over and just sit for several 10-15 minute periods. Any ideas as to what might be the problem would be greatly appreciated. It's very frustrating.