Late to the party, but as I also experienced the problem, in my case it was an issue with the permissions of the directory Opera was installed in. To further elaborate:
I typically install programs in a non default location (which is a different partition from the boot partition). Never had any problems with any program using this approach. However, after the upgrade to Opera 42.0.2393.85, I encountered the exact same problem mentioned in this thread. For good measure I switched the default app used for web browsing to a different browser. Neither Firefox nor Microsoft Edge exhibited the same behavior, so it was clearly Opera specific. I compared the applicable permissions between the Firefox folder and the Opera one. The Firefox folder had me as an owner, whereas the Opera folder had Administrator as an owner. After changing the permission to me, the problem went away.