Just wanted to share my experience with this issue so that it might help a select few with this annoying issue.
I don't claim to be an expert on this stuff but I have decent experience with computer troubleshooting throughout my life.
I recently bought macbook air 13" Mid 2013 model with the same connectivity issues. I would lose internet connection although the wifi connection to the router would be intact. I would have to turn off wifi and then turn back on and internet would work again. This was happening almost every 15 minutes.
I tried to install the software "fix" on the apple website that was supposed to correct the wifi issue. No dice.
Current software version is: OS X 10.8.5 (12F37). Next, I was setting the IP manually hoping that it would resolve some type of problem with renewing the DHCP with my router. That did not solve any problems.
Then I went into the router settings and restored all factory settings via access through the gateway IP address of the router on my browser and tried to designate a reserved IP for my MAC address. Still was giving me same disconnects.
Finally I hard reset my router (which I assume was the same of what I did earlier) via holding the reset button on the router after powering off the router and turning back on. Shut down my computer before doing this and booted after router was reset.
Now my current network settings are set to set IP manually with my router IP as :192.168.0.1. And my local IP as: 192.168.0.99. After that I have no had any disconnects for almost a week.
It seems like it had something to do with the hard reset on my router and less to do with the manual IP settings but something I did there did the trick. My router is being leased by Time Warner it is a SBG 6580. I havent tried connections with any other wifi routers. I will be interested to see if I am going to get the same issues with other routers.
I realize this won't help most people but it seems like it is definitely sometype of software issue with network drivers causing these disconnect issues since I was able to resolve my problems without any hardware alterations. Pinging my LAN around 2 ms. Speedtest.net I ping at 16 ms with full mbps upload and download speed I am supplied by my cable company. No disconnects is obviously the biggest resolution however.
Good luck all.