From the time people brought Apple MAC BOOK AIR (MBA) 2013 they are/were experiencing WiFi connectivity problem in home networks.
ISSUE: what happens is that you are normally using the net and suddenly you loose connectivity , but the WiFi icon shows connected . then you restart the WiFi in order to solve the issue but as this one is persistent it comes back again and hampers your download, browsing and other important work.
There were/are a lot of people posting this issue in apple forums but no solid solution was coming up.Some of the temporary ones were => switching the WIFI channel to channel no: 11, but it served as relief only for some few hrs.
SOLUTION: In these dark times there was not a word from apple's side, as MBA users hopes were dyeing out, suddenly there was a silver lining in the sky, after all apple wasn't sleeping as was assumed, but instead it was working on the problem and has finally come out with an official OS X Mountain Lion Update Specially to Solve the WiFi Issue.
And for all those who are still facing this issue just install the New OS X Mountain Lion updates released by Apple .