When you say "the circuit loses power", do you mean it trips in the breaker box?

The GFCI will only trip things "downstream" if they are connected to the "load" terminals on the back of the GFCI. If they are in parallel, the GFCI will not trip anything other than it's own outlets.

Is the refrigerator on the GFCI? It would not surprise me if the refrigerator didn't trip the GFCI when it was young, but as it got old the compressor kicking on started to draw more current (to overcome more friction as parts age).

Regardless of all that, I would probably address the Reversed Hot/Neutral issue first.