Fluorescent light turns off randomly?
The internals are pretty straightforward.  You're just looking for loose wires in connections, loose wires at a tombstone, etc.   

While you're in there, size up the wiring.  If there are 2 wires to every end of every lamp, that takes a different ballast than if there is only one.  Ballast swaps aren't too bad and they are also an opportunity to upgrade to T8 lighting. 

You could also think about going LED if the fix does not prove to be easy.  Get direct-wire aka ballast-bypass LEDs, don't get plug-n-play/needs-ballast LEDs.