Although it's a somewhat different situation, I encountered a similar "suddenly one string won't stay in tune" with a mandolin a while back. It started happening just before I noticed that the bridge had cracked and was slowly sinking. (Actually I figured it out when the bridge abruptly separated almost completely.)

Since it was at the beginning of our major festival, and no replacement bridge was available, I whittled one from a clothespin and made it through the festival. When the clothespin finally cracked (about 2.5 years later) exactly the same symptom appeared (briefly).

A sudden onset of failure to stay in tune, whether one string or several, could possibly indicate a "structural" slippage. Most gitar bridges shouldn't be subject to the same sort of cracking as my mando, but loose tailpiece screws, loose machine screws, or (hate to say it) a top plate crack or a loosening brace could be allowing the bridge to sag.

These are unlikely, probably, but a thorough and close insepection of everything hooked to the string or supporting any surface it bears against wouldn't be amiss. And you might find the real reason while you're looking.

John