Samsung Galaxy S2 wifi - Connected but no internet

My Galaxy S2 (ICS I9100G) connects to my home wifi but sometimes does not actually transmit data. I took it to the shop and they did a factory reset (which I could have done on my own) and then was told to take it home and see if it was any better. It wasn't. O2 tech support didn't really have much to offer so I tried various different online fixes. None worked. We got another router (for the back of the house) which used WPA2 whereas the initial router uses WPA. My SGS2 works absolutely fine on this new router. What's going on?