That is odd. It almost sounds like the higher current is heating something up to the point of failure. Once it cools down enough, the power comes back on and it just keeps cycling on and off. Have you tried something with a big power draw (like a hair drier) to see if it fails faster than just the pump? Unless you get better suggestions, I just start troubleshooting and ruling stuff out. If the GFCI isn't tripping, that means you probably aren't losing any power from the outlet down. Otherwise, current "in" wouldn't equal current "out" and it would trip. To confirm that, you can just disconnect the line from the GFCI to the lamp and test the outlet again. If the problem still occurs, you know you don't need to worry about anything going out to the lamppost. That narrows the search area down to somewhere between the box and the GFCI. If the problem magically disappears, then you know it is in the run from the GFCI to the light. If the problem sticks around, you have the connection at the box, a run of wire, a connection at the GFCI, and the GFCI itself as possible failure points. I'd rule out the connections first, then the GFCI, and save a new run of wire as the last resort.

Thanks guys. The system consists of autonomous switch replacements throughout the house which 'listen' for pulses sent along the neutral line. Technology is called UPB and is very common in home automation. Effectively this would be like installing a nightlight replacement in the outlet or something like that. Very low power draw device that does not control any load. Admitted I don't understand the inner workings of the GFCI system. Home is 3 years old and there are probably 12 GFI outlets throughout the kitchen and island area. I just wanted to pull power from one of them, hoping to simply 'jump' or connect the gfci from this outlet as if it were never there. I appreciate the advice and warnings though. I certainly have no desire to make the home unsafe.

"But I do have in my own house some circuits with multiple GCFI receptacles on that one circuit. In those instances, the GFCI is not connected for feed-thru, but protects only the receptacles in that particular unit, the others are connected the same way. Tripping of one unit affects no others." This type if installation has some real advantages. When something does trip the GFCI it is the one you just plugged into, and it is right there. No hunting for the GFCI. In my workshop I have a number of quad outlets each on a separate 20 A circuit. Each quad is a GFCI and a regular receptacle. The regular receptacle is on the load side of the GFCI right beside it. GFCI devices originally were breakers only, then receptacle. They were so expensive initially (around $35 each) that the first few code revisions allowed a single GFCI proptected circuit to cover bathroom receptacles, outside receptacles, and even unfinished basement receptacles. The dedicated 20 A bathroom circuits came latter. In many cases installations that complied with code initially remain grandfathered. Some exceptions have been made for bathroom GFCI devices and kitchen counter spaces in many local codes. The use of GFCI devices in these spaces is really worth the protection. One of the biggest problems with the HI community is a lack of knowledge about plumbing and electrical codes changes and when they occurred. Even the RE column in the Washington Post (writer recently died) was uninformed about GFCI circuits and their operation. An HI squawked an older house kitchen counter outlet for not having a ground. The seller had GFCIs installed in a 2 wire circuit with the required stickers. The purchaser complained the job was 'not to code' since no ground was present. The advice columnist agreed. It is fully code compliant to install GFCI receptacles on 2 wire circuits.

txmat -- re your question about GFCI units with a "built in delay," I suspect those are for higher voltage industrial applications and are for protecting machinery rather than protecting persons which is what residential GFCIs are for. What you might want to look for instead is (I think) called a "hospital grade" GFCI. Not time delayed, but more robustly built and less likely to be tripped by the fridge. You probably want to look for a 20 amp version. A brand name is Leviton. (There may well be others, that's just the one that came to mind.) That should help with a search for models and vendors. So, use one of those to replace the existing GFCI per Weed's suggestion. If one of those does not solve the problem, you might try posting your question in the Electrical Wiring Forum here. Also, if your "new to you" house/garage was built before 2010, there may be lesser requirements for GFCI in the garage and you might be able to have the fridge circuit without a GFCI. My recollection is new construction now requires GFCIs for absolutely everything in a garage (except maybe dedicated light circuits) but that prior to 2010, the NEC and IRC allowed you to have a dedicated non-GFCI circuit for a freezer or fridge. So, maybe permissible if you plate over the existing first outlet and remove the outside outlet. (No help if that's the only circuit to the garage). If built prior to, I think 2003, codes may have permitted that line go to other outlets as long as the downstream outlets were GFCI. I don't claim to be any kind of code expert, but hopefully this this helps for further research and is another reason to check out the wiring forum.