I'm seeing the same problem with my ipad mini. I have a Cisco / Linksys E1200 router which my ipad2, iphone 4s and ipod touch 4g all connect without problems. My problem started right around Christmas time when I updated to IOS 6.02. It had been working flawlessly until then which I've spent many hours trying to figure this thing out.. including resetting, restoring, resetting network settings, setting up a new wireless lan with a different wireless router. Changing wireless settings, trying B/G and N network settings. I can connect if it's about 3 feet away from the router but anything past this, the wireless bars are still full (at 3) but if you try browse internet or were streaming video.. it loses connectivity. If I renew IP lease on the connection as it shows that it's still connected... it will renew to a 169.x.x.x address instead of the 192.x.x.x address.
I took it to a Simply Mac store and since it connected to their network.. they said they could not do anything about it. (Simply a waste of an hour of time and gas).. of course that's nothing compared to the many hours already wasted on troubleshooting this dang problem which appears to be a hardware problem which Apple will not admit.
I won this at a work party so I can't even take the dang thing back to a store. At this point I'm almost to the point of using it as a book stop and shelf it.... argh. Apple products used to 'just work' -- looks like they're losing their reputation as the internet is flooded with people having problems like this.