Every so often, after I've been practicing a lot for days, I'll get to a point where my fingers just won't work right. For example, tonight I was trying to double-pick the G major pentatonic scale with a metronome. My fingers were fumbling with the strings, sometimes not hitting some strings at all, and generally just not working.

Has this happened to anyone else here? It scares me a bit.
Sounds like a bad playing day to me it happens to everyone more than you think. The good thing about this overtime the better you get the more consistent your playing will be. Even on bad days of playing or if you'd like off days.
Sounds like fatigue. There is a limit to how long you can keep playing before muscles get tired. One thing you could think about is whether you're actually gripping/pressing more than necessary. Almost all of us tend to do this.
Time to take a break,Have a couple of days rest from the guitar.Should be right as rain when you pick it up again.Don't wanna strain those tendons.