An intermittent thermal fuse would be way down on my list of possibilities but is easy to monitor by measuring the voltage across it (CP3, CP5) when the failure occurs. If the secondaries all die then the fault would most likely be on the primary side as the secondary windings are each isolated. You could have an internal connection issue where one of the flying leads is soldered onto the actual winding. My first thought though is to suspect the supply side - in particular the terminals and their joints on the PCB.
Are seeing 120v at the centre when the transformer fails?