My chainsaw clogs up cutting palm and banana trees

I've cut Mexican palm and banana trees with my chainsaw and I am having trouble with the clutch area getting clogged up after a few cuts. Apparently the fibers of these plants builds up in the clutch area of the saw which in turn causes so much friction that the saw stops running. I end up taking the side cover off and cleaning out fibers and this really slows me down.

What to do to prevent this?

I have an older Husqvarna 242 chainsaw.