I am jumping onto your thread a long time after it concluded. I just bought a '98 Archer III with a KAP 140. I get the trim fail (PT) message about every fifth flight, right after takeoff. So the electric trim is out until my next flight. I hadn't thought of shutting off the avionics until you mentioned it. Had the trim rigging checked and lubricated, but no improvement.
Wondering if you learned anymore on the topic.
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Thanks.