My thought is that if you aren't getting power from the fuse box (when this happens), then the issue is going to be from the fuse box and back to the battery.... somewhere in between those two points. Since you're not losing power to other accessories (headlights, wipers, radio, etc), then you can pretty much eliminate the main power source, which is the battery, cables, and power supply to the fuse box.
This is, of course, an overly simple way of looking at it, but I can't think of any exceptions that this theory doesn't apply here. I'm presuming everything you're telling me is true, which is why I mentioned "user error" in regards to where you were probing the fuse box. Hope that make sense!
So basically, I would begin trying to test behind the fuse box. Inspect for loose wiring. You very well may have been on the right path in suspecting the relay. If possible, try checking the feed to and from the relay socket when it happens. Intermittent issues are always a pain to diagnose! You can probably figure out a way to rig up some test probes/wires. I believe they make something for this, but in a pinch, a sewing needle strategically stabbed through a wire can provide a good contact point for testing.
I would start with a careful inspection of this area, though. If you can connect a light tester or bulb of some sort to your window motor, you can watch it while poking around in the wiring behind the fuse box and under the dash. Again, just have to get creative here. You could even have a partner standing by with a meter to tell you when something changes, while you're upside down under the dash.
