This exact problem occured for me aswell some time ago. I also have the S2. The problem started some time in february. This is what I've found out about this problem:
-The problem seem to be System Data using the appstorage and growing in size. We won't have admin rights to even view it's content. When installing an app like DiskUsage to view appstorage, it just says System Data without further explanation. On my phone it's currently at 1,4gb. My girlfriend has the exact same phone and she's owned it way longer than me, she has no issue with this, when viewing her appstorage in DiskUsage it's only 40-60mb.
-It seems to be an android issue rather than a S2 issue. I've googled this a lot, and I've seen HTC-users and Samsung-users mainly being affected.
-I did try: Clear cache from boot menu, move apps to SD-card and all the other straight forward suggestions found online. I even factory-reset my phone during the Easter. Surely enough, the System Data disk usage was wiped and down to 20-40mb as it should be, but now, 2 weeks later, the System Data chunk on my appstorage has eaten all my free space again. I even read somewhere online that another user tried getting a new phone from his supplier, and even that didn't stop the problem. I don't know if this last part is true though.
From what I can tell (through second-hand-knowledge, of course) is that it's most probably just logs that keep filling up the appstorage, and the only solution MIGHT be rooting the phone and deleting these logs. The cause I've seen suggested the most is Wifi-logs and/or application-stopped-responding logs; I also picked up the filename anr_history.log, but I don't know if that file is for HTC-phones only.
From what I can tell after hours of hours of googling, there is no real solution to the problem. Either factory reset every 2 weeks, or root the phone to delete logs as they grow in size. But I'll contact the store where I bought the phone anyways, even if I don't think it'll solve the issue after reading the threads I've found online.
I guess this thread is about the same problem. Same workaround, though: Root!
[Q] wifi error data log - xda-developers