If you feel the engine is running hot, it's raather foolish to NOT clean the cooling fins. Especially since that's considered normal maintenance.

When the problem occurs, loosen the gas cap for a couple seconds. IF that makes a difference, the vent is clogged.
Else, you may have a heat sensitive ignition coil.

Check the condenser in the spark system. What you are describing is exactly the conditions that occur when it fails. Works fine for a period and then dies. As it continues to fail the running period will become less and less until it will not start.

***'Check the condenser in the spark system."***
I do not see how this could be offered as a possible solution, considering that the OP does not even identify the make of the machine nor of the engine, let alone specific details of year and model.
Condensers HAVE NOT been featured as a component on small engines since the demise of ignition systems with contact points. In most cases this was over 30 years ago.
Perhaps you are thinking of some other component, but calling it a condenser.
But still, even that is a pretty specific suggestion to such a broad, vague, and generic problem description.

This post was edited by mownie on Wed, May 28, 14 at 9:49

My 2001 JD 155 Kohler engine had a condenser in the ignition circuit. It went bad and it took several months, and trips to the dealer to realize what was wrong.

Once they replaced the condenser coil, the tractor worked perfectly. At the point they replaced the coill, they had replaced much of the ignition, but until then nothing helped.