Small Engines (Lawn Mowers, etc.): Briggs 16 twin runs rough when hot, head bolts, compression test

Question
Briggs 402707, 1205 01.
Ran perfect on start.  After 45 minutes of mowing began running rough and surging.  I could not get any reaction when I adjusted mixture screw.  Removed carb, soaked, and installed rebuild kit.  Ran great 1st use, thought I had solved it.  2nd time was a different story.  Back to square one with the uneven rpm after 45 min. of mowing.  Where do I go next?  Many thanks -

Answer
Does your carb have the electronic anti-afterfire solenoid?  When was the last time you replaced the spark plugs?  The last time the valves were serviced?  Head bolts torqued?  Have you performed a compression test on the cylinders?  Are the fuel lines, and fuel pump lines in good shape?  Are the intake gaskets good?

Let me know.

Eric