I'm another vote for a fuel issue.
As well as pump or filter, it could be a (partially) blocked vent, since it only happens after periods of higher power operation.
Possible but less likely (maybe even remote) : intermittently weak ignition, something loose that can flop around and partially block airflow through the airbox, accidentally dragging on the foot brake.
Getting a touch of water in the gas through a poorly sealed cap *could* explain the symptoms, but usually the engine will outright die, and you wouldn't see it only at high speed, unless he happens to start up and get out on the open road pretty well right after the rain several times.
Clutch slipping would be punctuated by high revs, which he didn't report, so that seems to be ruled out.