Hmm. The FI relay seems to typically cause a prolonged no-start problem, but I still wouldn't discount it. Especially since it's free to re-solder if you're decent with a soldering iron. I would definitely try that first.

Beyond that, I think that you're looking at some kind of bad electrical connection pertaining to fuel injection or ignition, but I don't know what. If it were something like a bad fuel pump, you would have warning before the engine quit entirely. And if it were a more major electrical fault, (like corroded battery cables), your radio probably wouldn't continue right on playing. I suggest that you look for all the chassis grounds that you can find and clean/tighten them. At the very least, you'll be preventing future problems with that tactic. Good luck.

Tim