I have the same problem.
It's completely random. Sometimes I get some results (either from search or from history) while I type, but even after few characters it greys out. Even if I delete it and start typing again it stays like that. And it not only affects search - I'm trying to enter whole URL and hitting enter won't do anything.
Additionally I noticed that it starts to work when I enter Private mode.
I tried to disable ALL extensions but it didn't help. I'm also not keen to reset it or reinstall and starting from scratch.
And I have to say it's a big thing cause it makes my Opera unusable. I can only go to some sites through history or bookmarks. If I have to type it works after I open 7 or even 10 new tabs.