Anyone encountered a situation where a Saved Search suddenly starts just refusing to run and gives an Unexpected Error?

It's hard to tell. It's mainly to do with wrong formula

I've had that happen if I have disabled features and now fields that were part of the disabled module are no longer "there" so the saved search returns an error. Have you turned off anything in Enable Features recently?

Not in my case. But from what you say about disabling a feature, so it's expected to have received errors. I would remove the formula lines and preview until the problematic columns are found. If know the problematic lines then remove them