Using Opera Mobile 9.5 (Stock VZW). I never have problems with it closing. I have ran all sorts of stuff while it was left open. Only problems I ever get with Opera are.. improper
JS loading (eg, Manage attachments doesn't always show in forum), random websites causing crashes, and the Opera white screen of death. In case you didn't know what that was, it's where every page loads turns into a white screen with nothing on it, forcing you to have to kill it in Task Manager. Other then that, PPCGeeks loads quite fast. Using OM 9.5 right now to post this.