I have the Galaxy S II myself and have run into this pretty frequently myself, so I do know how annoying it is. We currently do not have a known issue for the GSII in regard to this, though.
There are a couple of steps that I can recommend. First, call Technical Support. We can troubleshoot the issue and see if there might be a software or setting causing the problem. If we are unable to fix it right then and there, we can gather information and escalate it up to Samsung for tracking and investigation purposes.
Second, and this is only what I have tried and seen a bit of difference, AFTER contacting Technical Support, if the issue remains there is a way to disable a feature called "Fast Dormancy". You can read about that here:
and again, here:
This will help with battery life as well. Keep in mind, I am only speaking from personal experience regarding disabling this feature to assist with the internet connection "timing out", for lack of a better term. This is why I highly encourage you to call Tech Support to escalate the issue further.
I hope this helps you out!