Check vent in fuel cap.
New fuel filter.
Make sure seat switch is fully plugged in and adjusted to insure good plunger travel.

Another possibility is the fuel pump is weak.
A restricted filter or weak pump may result in enough fuel flow when NOT under load, but allow the carb bowl to slowly run out of fuel when under load.

You might also check the quality of spark with a cold engine and again when the problem occurs.
You may have a heat sensitive coil(s). IF so, cleaning the cooling fins might make a difference.

This post was edited by bill_kapaun on Sat, Jul 26, 14 at 21:48

I have seen this exact problem on other 2 cylinder mowers, do not know if yours is 1 or 2 cylinders. If 2 cylinders, remove the valve covers and look at the pushrods. The pushrods often bend giving you 1 good and 1 useless cylinder, revs OK with 1 cylinder but no power. Another way to check is to pull one spark plug off at a time and run the engine. If it works with one side on but not the other, you have a dead cylinder and again I would suspect the pushrods, especially if a B&S engine