The Alerting service was indeed down - silently so, and apparently due to "time travel" of our SW server. To quote SW support (highlighting mine):
If your server was not involved in any kind of time travelling, it is possible that the server time was different for a short time when the Alerting service started and it was set back, and the next database check was scheduled to 4:40am.
In other words, if you deliberately or accidentally send your Solarwinds server in the future, and it comes back alive, expect the Alerting service to stop working until that future actually arrives. The reason is because the service schedules database checks and doesn't verify the validity of that scheduling. E.g. if the next scheduled check is somehow far in the future, the Alerting service simply stops working.
Isn't it fun? (I wonder how it handles daylight time clock rollbacks. Stops working for an hour? Maybe not if the time is absolute, i.e. based on GMT.)
Even though the "resolution" isn't to my liking (I'd prefer SW to be a little more aware when things break and stop working), I have to give kudos to SW support for fantastic troubleshooting skills and speedy and professional responses.