my Honda 5.5 engine fades after a few minutes?

I have a mower with a Honda 5.5 engine #GXV160-A12 which starts easily and runs well - but only for a few minutes. Then, without warning or complaint, it dies. It is almost as if the kill button had been used. It restarts after a short rest. After a few iterations of this game, it will run normally and I can do the lawns. What could I look for to solve this?