Why is my new mid-2011 Air dropping wifi signal which old 2008 MacBook can hold? And is this related to my complete machine failures?
Is your old MacBook (the one which doesn't drop connection) running Lion or a previous OSX release?

The reason why I'm asking this is that I suspect it might be an issue with Lion, and not with the Air.

I have an early 2009 17" MacBook Pro that never dropped Wifi while at home, ever. Since upgrading to Lion 1 week ago, I lost Wifi 3 or 4 times, but only for a short period (it automatically reconnects after a few seconds).

I am confident that it's not a router failure, as one of the time my MBP dropped wifi I was downloading a file on my wife's iMac (over Wifi) and it didn't drop.

Fwiw, my router is a 2nd-gen (dual-band) Time Capsule.