I've seen this issues is quite old. It was bothering me so much that I actually switched to Firefox. Ironically it also happened in Firefox after syncing. I found out the problem was that the browser deleted cookies on close. (I guess it imported that setting from my sync).
So I went to Opera to see if it was also the case. (It was)
Go to cookies settings opera://settings/cookies and uncheck "Clear cookies and site data when you quit Opera"
Hope it helps