I have the same problem. Tried all the solutions mentioned above but no go :-( Just as the others, I have the problem that it won't connect at startup. Get a self-assigned IP address. But if turn off the WIFI and then turn it on again it works fine.
Any other ideas? This is a problem I just started noticing yesterday, though I rarely restart my computer, a 2012 MBA with OS X 10.8.4. I also have a 2011 MBP at home with OS X 10.8.4 but there is no such WIFI problem on that computer.
Another interesting note. My home network consists of a NAT router from my ISP connected to the internet with WIFI off and then two Airport Expresses, one on each floord, set up as a roaming network. It all works fine, except for this little oddity with the MBA. Upon closer investigation, it also turns out that if I start the MBA when I am close to the downstairs Airport Express - a 1st Gen - then there is no problem connecting at startup. But if I start the MBA near the upstairs Airport Express - a 2nd Gen - then the problem occurs.
Can't seem to get my head around the problem. Any help would be appreciated.