I think trying a different brand of GFCI is a good idea. In my experience,
in my house, I have had some that fail and just trip, no matter what's
plugged into it. Buying a new one solved the problem. I have also noticed
that the number of years they last varies from one GFCI outlet to the next.

In all cases, when the outlet needed to be replaced, it would continually
trip to the point it didn't do any good to have anything plugged into it
because it wouldn't get power. That is really good though, because you want
the device to fail that way rather than to fail, still supply power, and you
not know about it.