I recently had wifi connectivity problems with a new macbook air and thought I'd share my experiences here. First, some background.
Years ago, we had a wireless network consisting of an Airport Extreme (the old one that was somewhat dome-shaped) and an Airport Express (the old one that plugged directly into the wall). This worked fine for a late 2006 white Macbook (OS 10.4, later 10.5) and an older Powerbook, but my Thinkpad T42 (win XP) would not stay connected reliably, dropping the signal at random times and requiring multiple resets and other annoyances. So after a bit of research I replaced the whole network with a pair of Linksys WRT54GLs flashed to DD-WRT v24. One ran in regular AP mode and the other in repeater-bridge mode so as to get an old (non-wifi) imac and the laser printer downstairs on the network.
This DD-WRT configuration was one of the most reliable installations of any kind of technology I've ever used - I had to reset the routers maybe twice in three years, and neither the above white Macbook nor the Thinkpad, nor a November 2008 Al macbook (OS 10.5, later 10.6), nor a 2011 Macbook Pro (OS 10.7) ever had any problems staying connected.
Unfortunately, when the November 2008 Al macbook was replaced a few months ago with a 2012 Macbook Air (OS 10.8), the MBA would not stay connected reliably (although it had no problems in other places where it was regularly used, e.g. office wifi networks).
It's worth noting that the user account/data were copied via the Apple migration utility from the 2008 macbook to the new MBA. One theory of MBA problems is that (sometimes) they are caused by settings getting ported over from an older OS improperly, but that doesn't seem to have been the case here, I don't think.
All of the following - gleaned from this and other threads/sites I found while trying to troubleshoot - were tried, but to no avail, or at least no regular avail (i.e. a restart would sometimes work, but only for a while, or sometimes not at all)
-disconnect / reconnect to the wifi network
-use network connection troubleshooting wizard
-turn wifi off/on
-DHCP release/renew
-reboot the MBA
-change the wifi channel
-change the wifi security method (e.g. WPA2 vs. WPA)
-change the network name
-change from a/b/g broadcast mode to forced g-only or b-only
-clear the SMC
-manually delete user/system keychain entries related to the wifi network in question
-disable IPv6
-set MTU = 1453
-add manual DNS entries (cf. picking these up via DHCP)
-add new location in location manager
I did not try the following, either due to lack of time or seeming inadequacy / hackishness of the solution:
-have Apple replace wifi card in MBA
-alternate wifi hardware (e.g. USB adapter)
-genius bar visit for troubleshooting generally
-keepalive shell script running in background
I should add that in the midst of tinkering with Linksys router settings, the macbook pro 2011 started having connectivity problems as well, although it never had any previously.
Especially in light of this, and after at least 10 hours of researching and troubleshooting I started to consider more drastic measures - changing the firmware on the Linksys routers or buying new routers altogether.
DD-WRT seems to have drifted from the open-source philosophy and had some security holes a while back, so I did not want to just upgrade to a newer version of that. I also didn't want to bother messing around with Tomato because I wasn't sure different firmware on the same hardware would address the problem. I then considered buying new non-Apple routers and flashing them to Tomato, but it seemed this might not absolutely fix the problem either, although I wouldn't mind upgrading to 802.11n (the Linksys hardware only supported 802.11g).
Ultimately I just drove to the nearest Apple Store (about 30 minutes away) and bought two Airport Extremes. After the usual setup, the MBA began to work normally again, and has functioned perfectly ever since (no issues with the Macbook Pro 2011 which had been fine on the old configuration as well). One would hope Apple laptops would work well on Apple's own wireless gear, and it seems to be true at least in this case.
I can't say for sure alternate firmware on the old Linksys hardware wouldn't have worked, or that Tomato/DDWRT/other alternate (or even stock) firmware on some new non-Apple hardware wouldn't have worked. But ultimately I ran out of time to keep troubleshooting.
I think at least in this case I can rule out the idea that the power management aspect of the MBA was cutting power to the wifi card and thereby dropping the signal (another theory I've seen at least for some MBA wifi problems), because if that were the case then the problem would have persisted even after switching to the Airport Extremes. I haven't looked in fine detail at how various wifi routers / adapters vary in their implementation of 802.11b/g/n, but I can only surmise based on this experience that they are not all perfectly equal, and that the risk of conflicts increases the greater is the age between (at least some) wireless routers and (at least some) wireless adapters.
In summary, if you've been having this kind of problem, you may save time and headache (although not necessarily money) by simply trying different wireless networking hardware. And if that doesn't work, you could always return it.