My guess is the clutch shaft needle bearings. Most clutches are two pieces of metal with a spring around it in a housing. centrifical force forces them to over take the spring pressure and lock against the outer housing. result is chain spins. IMO the needle bearings are shot heating up and reducing the RPM of the clutch drum which causes the two metal pieces to seperate from the spring pressure and alowing the clutch to go into the free wheeling mode when the saw is at idle or you get the chain stuck in a log. Take the clutch off you should see something wrong again I think it's the needle bearings.

It could be many things, but one option for you is to try running the chain a little loose, when it heats up it will have a little extra slack to keep it from siezing up.

I suggest you remove the chain and see if it will shrink & expand length like a accordion. If so. It has not received enough oil and it is shot. It tries to climb to the next tooth on the sprocket & binds up. If you continue to use it, either the chain or the front sprocket will break.
Your sprocket is likely to also be worn out.
I stock any part you might need.
Bill Walcott
785-562-3539