The only thing that a GFCI does beyond a regular breaker is to monitor the current going out on the hot and the current coming in on the neutral. If there is less current returning on the neutral ( 0.003 amps or so) it trips. If there are poor connections, high resistance, reversed polarity or open circuit a GFCI will still work just fine because the current out will still match the current returning. If you are standing on a dry rubber mat and grab the hot in one hand and the neutral in the other the GFCI will not trip either. ONLY when there is a path to ground from any part of the circuit on the LOAD side ( either hot, device being powered or return neutral) will a functioning GFCI trip. Try to isolate and troubleshoot on the load side of the breaker to find the problem(s) Poor connections ans poor shore power is not good but this is about current finding a path to ground not on the proper path.