Several possible issues.
If you are right and it is vapor lock, the causes are that the engine is heating up the fuel line. Check to make sure that the fuel lines are not close to any part of teh engine that could heat it up.
The engine could be getting too hot because the engine is running too lean. Over the years ther may have been dirt, gum and varnish build-up in the carburetor. This eill either plug up sem of the small passageways or at leas restrict them. It still may run, but would run lean causing it to run hot.
Make sure that you are running the engine at FULL spead. Running at less than full throttle can cause an engine to overheat.
You actually could have a coil or condenser(id so equipped) breaking down after it heats up. You may have to replace the coil, points & condenser (or electronic ign if so equipped)
Last but not least. The gasoline MUST NOT BE OVER 30 DAYS OLD. Old fuel will cause many problems.
Also, You must use good fuel of at least 89 octane. Gas has changed over the years so we need to use better fuel.