Its not confined to private pilots, a number of years ago I had to fly on a regional service from Adelaide to Port Augusta.
It was a late winters afternoon, the single pilot had leaned the engines on the Navajo, switched on the autopilot, sun was streaming into the cockpit.
I was sitting a row back, watching the progress of the flight, when I noticed the subtle head bobbing..
Yep he dozed off, for about 5 mins.. I thought mmm... thats professional, do I wake him or not?
I was about to get out my seat and poke his shoulder but he woke up.. looked at me, mumbled something and went back to fiddling knobs.
He managed to stay awake for the rest of the flight, and avoided me at the conclusion.