All kinds of possibilities for the cause... but it SOUNDS like you are running lean.

A hard to locate cause is a pinhole in the flexible line inside the fuel tank. The fuel level in the tank goes below the pinhole and suddenly the engine won't run right. Runs fine with a full tank ever time. This one can drive the local engine expert nuts. (and its a good reason to have the ability to easilly pull the fuel tank from any model.)

Dirt in the fuel system tends to accumulate inthe needle valvve is you don't have a fuel filter. That will make the engine go lean. (but it will be impossible to retune it and make it work until you clean out the needle valve.)

A split muffler pressure line can make the engine run lean... and it will get worse as the fuel level goes down.

Too heavy of a prop can make the engine run hot... too small or too large is not good, but you can adjust the fuel mix to prevent overheating with the undersize prop easier than with oversize.

*****

My bet is a fuel line problem. 5 min is too long for it to run properly with the wrong size prop. It is also too long for it to run properly with an excessively lean fuel mix. Sounds like its running too well and consistantly for it to be dirt in the needle.