I'm thinking a ground issue too. IF your settings IN the cobra weren't accurate i don't think it would be as much of an issue as you stated. Try the ground then call cobra if it doesn't help.
My brother had the same exact symptoms you described it was on a VTX 1800 and his was tuned in a shop, he thought it was one of the wires going into the module was intermittent which a friend of his had that problem, but
it was the ground. He cleaned the paint from under the screw reattached the wire then painted it with clear touch up paint to prevent corrosion. His bike ran the rest of last summer without a problem.