Glenn,
GFI's are prone to nuisance tripping from electrical noise. Perhaps when both operators are being used they are causing enough garbage on the line to cause a trip.
You could try installing GFI's in such a manner that the garage door receptacles are not being protected by the GFI's. I don't know how many new receptacles this would take, but you can get them for as little as $6 or $7 apiece. You'll have to work ot the cost versus aggravation factor yourself.
Tom