Cast your mind back, Kostya to the other weekend, when we worked on Ann's duplicate email issue and you said you'd noticed that there were some IMAP search errors in the log file.
Well, you were spot-on right - there were - and the culprit is Smartermail who apparently have a bad (non-existent?) IMAP Search implementation and no intentions in the short to medium term to fix it (even though they know it also affects IOS users!)
Now, granted there's nothing you can do to fix their problems, that said, it would be nice if we could have a setting either in the global Search settings or preferably as an account setting that would allow you to turn off the ability to perform a network search.
Doing so would at least allow the local search to function without displaying any error messages.
Thanks!