I finally got back to work on the Rincon 680. I pulled the top off the engine and discovered that the cam is wore just like I suspected.
I am still not sure why it wears out? In the first photo you can see the cam sitting in the "tin bathtub" full of oil. It is definitely getting plenty of oil. There was no noticeable wear on any of the other parts.
Here is the cam and followers removed from the engine. You can see the follower on the right has a definite concave shape to the contact surface, it should be flat. Both the intake and exhaust lobes were about .075" short.
I don't know why this is happening, but it seems to be a common problem on this engine. An after market cam is available for about the same price as a new Honda original part. I am going to recommend that to the owner.