Sounds a lot more like a cold solder joint(s) on the header pins or a component. Re-flow solder on all the header pins on your power supply board first.

Your symptoms still sound related to a failed connection and not a failed component.

Typically, faulty components are constant (yes, even capacitors) while faulty connections come and go with things like vibrations and heat.

While it's always a good idea to replace old capacitors.... caps specifically do not typically "work for hours", then fail and then "work for hours" again. When they fail or begin to fail, they always show "build up" and "trickle down to failing" symptoms that are consistant. Your abrupt/sudden/random symptoms don't fit this very well. Do not overlook the obvious.

Next time the game is working properly, carefully wiggle the connectors to see if you can get it to crash on purpose. If you do, address those connectors/pins where it failed. Intermittent problems are the most difficult to track down but you can do it if you are careful and patient!