Thanks for posting an update
The ignition key should not be the cause, as it is only in the game when you want it to run and the OP says it resets over nite when the key isn't in the game... Just think of what it would take to reset the computer/clock/etc over night when it is just sitting there 'off'...
The fusible link is just that, a fuse via a length of special wire. Once it is over loaded, it is gone and there is no reset like a circuit breaker. Unless things have changed on newer vehicles
A remote possibility if it is within the fusible link...an intermittent and is akin to load dumping the system
Good to hear that the battery is replaced, but the alternator and other chips that saw load dumping are still a potential problem that might create another load dump situation. Mainly the alternator diodes and might take down the new battery in short order
As Burbman stated, the high voltage spikes from constant load dumping will create shorts inside the battery to manifest itself in a flaky battery...that then contributes to more load dumping of the whole electrical system (voltage spikes)
Think of taking a 110 line and touching the electrical system on a regular cycle and only just a moment. That is what load dumping is...spikes of that kind of voltage or even higher. That will punch holes in the silicone chip...that will either open and/or short
Good luck