I am thinking that the wiring of your neighbor outlet is not correct and hence my suggestion for the tester.

It's fairly puzzling that it would work for 4 years and then suddenly stop working if it was wired incorrectly.

First thing to check anytime the GFI (Ground Fault Interrupter) pops is the resistance value between the heating element electrical lug and the mounting hardware of the element. Do this with the machine unplugged and with the lugs disconnected from the leads. If you get anything other than an infinite reading you have current leaking from your energy source to ground. It is this split of currents, some back through the neutral wire and some back through the ground wire that causes the GFI to trip. Remember that the neutral and ground are bonded at the panel and only the neutral, insulated from humans, is supposed to carry any current. Even if you get a large ohm reading it is time to get a new element. The condition will only get worse and will not "heal" itself. I remember as a kid the neighbors washing machine, Saint Vincent DePaul special, that would shock the crap out of you if you touched it when it was on. Oh the days of fuses and two wire circuits with no ground.
And as far as why it would trip on one outlet and not on the next it is a function of total resistance in each run of wire. If there is a larger amount of resistance in the ground circuit of the second outlet the current is going to want to travel the neutral wire. Heck, the ground may not even be hooked up on the second outlet. I always check the appliance first and then check the GFI.
jpboyt

In what probably isn't a surprise to anyone - a new heating element resolved all the problems. After 5-6 years it was likely just time.