After the release of Opera Mobile 9.50 beta 2 Fingertouch, I've been using it a lot on my P1i for browsing for hours. I notice a strange behaviour in my P1i when I've browsed the web for long through it. My phone doesn't notify me of any SMS sent to me. Neither with the tone, nor with the icon in status bar. When I restart the phone, the new SMS is displayed. I wouldn't have noticed if I hadn't turned my phone off one night before going to bed when I was too tired. In the morning when I booted the phone back I got two SMSes that were sent to me three days ago. lol! I generally didn't use to turn the phone off for weeks. Whenever necessary I used to set it in flight mode. But now I do that every night before going to bed.
Well, a probable reason I guess is that the new Opera Mobile is a RAM hog, and when the RAM goes too low while web browsing, the phone shuts down the SMS client process that listens for SMSes, in order to free up some RAM. Whatever may be the exact reason, it should be fixed by Opera.