Starting overnight all my scheduled refreshes have been failing. Manual refreshes also fail. I can refresh from the desktop app, and I can republish with no trouble. Seven datasets have failed so far. They all give the same error message in the refresh history: "Exception of type 'Microsoft.DataProxy.Exceptions.HybridException' was thrown." The only other thread I can find on here asking about that error message never came to any conclusion about what caused it. So that's...super helpful.
All of these datasets have previously successfully refreshed at least once since the last time I published them. Most of them were published months ago and refresh multiple times per day, so there's nothing new that should cause this. My gateway is online and visible from the service.
Edit: apparently there is a known issue causing this. It's on the Power BI support site, even though nobody has bothered to put up a service health announcement on Office 365, which is also super helpful. Nevermind, I apparently can't read. That's Northern Europe. I'm in North America. So this is still a mystery.