A short won't trip a GFCI breaker unless it is a hot to ground short (also known as a ground fault). A "normal" hot-neutral short will trip the circuit breaker. GFCI's trip when the current in the neutral is different from the current in the hot line. That's something that usually doesn't change during operation unless there is movement that causes a ground fault. 99 times out of a hundred a situation like this is a bad GFCI.
A possibility is a damaged neutral wire or loose connection that is heating up and conducting poorly. Worth a look.
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