I have a 15 amp 240 volt, ground fault circuit breaker (special order and pricey). I have this connected via 14/2 wire to a deep well pump submersed into the lake, and a 500 watt baseboard heater. This has been connected for 16 months with no problems. This weekend I could not get the circuit breaker to work without it tripping. I tried disconnecting the wires to the circuit breaker (no load) and it still tripped, I tried moving it to another location on the panel box still tripped. As a last resort I took out the gfi circuit breaker and connected a (on hand) 20 amp 240 volt circuit breaker. It did trip once but worked fine for the rest of the weekend (Saturday and Sunday). There has been record rainfall at the cottage the last couple of weeks and there have always been what appears to be voltage drops on the service as the lights will dim with no other loads (no motors or heavy voltage draws starting up when the lights dim.
Any ideas? I have checked the line at all locations looking for animal damage or obvious shorts (electrical boxes, box connectors, etc. no obvious shorts.

This is not a faulty gfi. The more it rains the more conductive the ground becomes. I am surprised to see a well pump on a gfi. The long run will induce ground currents. The more conductive the ground is, the more easily current will flow until the gfi trips.

Most power supplies for water supply pumps do not require a gfi breaker. I would check local authorities to replace the gfi with a standard breaker and ground relay instead (if they want some indication of ground current).

The ground current is not a fault; it is normal behavior for this type of circuit.

I did not get that the circuit is long. The supply voltage is in question thou.

Voltage drop or sags will cause the current to raise slightly, and if left running long, may heat the breaker and trip due to an apparent overload.
And/or
The motor may not have the proper voltage to over come it's workload, and put the motor into a "locked rotor" condition, which can cause the amps to increase 6-10 times of running load.

The voltage drop may still exist and not getting better , but worsen due to a loose or corroded connection somewhere in the utility or home service equipment.

Or there is a ground fault, either in the motor due to a leak, or the heating element is wet or corroded. (I have to assume the heater is not in the lake with the motor).

Since the breaker still trips now with no load or wiring connected, indicates the GFI breaker is now probably defective.

The fact the standard breaker did trip indicates there still is a problem, but a standard breaker is not as sensitive to minor fluctuations,such as a GFI is.

The standard breaker must have overcome the fault or the fault is cleared enough to heat the unit up to eiminate any moisture inside.

The answer you received so far is inaccurate for your situation. If you are interested in reading a brief explanation how a 2 pole 240 volt GFI breaker works, see:

http://expert.ecmweb.com/resistance_...rcuit-breaker/

So, in simple you can replace the gfi with a 15A (or 20A if its 12/2 conductor which I suspect) 240V standard breaker as I have suggested, or

You can pull the pump, rebuild it, dig up the supply line and oversize all the conductors to compensate for voltage drop and buy another one of those 15A 240V GFI breakers.

Either way, your problem is solved!

You may also want to separate the baseboard heater on a different circuit to free up power to the pump. The pump deserves a dedicated supply (the tripping of the breaker may also be due to the cold days that now activate the 500W heater).