Sounds like a loose wire,
Works a few moments until the heat causes the wire in the junction to expand and break contact.
I am assuming that if wait a few moments to half an hour that the power comes back on...
First isloate the wire run, turn off all breakers except for that one and then test all outlets and lights to see if there are devices installed before the GFIC
Hopefully there will be a loose wire in a outlet box.
On occasion the boxes can be in the attic or under the home. Code says that the junction boxes are to be accessable but that does not always happen.