I do have the same problem.
It happens in the beta version, portable and also in the production version.
Most of the shortcuts, mouse gestures, keyboard strokes stop.
The only solution I have so far is restarting opera.
In my case, I note this happen when the pop-up blocker react to some sites that are comum to open a lot of pop-ups.
Hope this help you find a solution.
Keep making great software, and it is amazing if you figure out why this problem happen.
All the best