Please allow me to ive a thought about worrying about the router.
As far as I am concerned, I admit that the type of router, or the config of the router, might make a difference. I only have the intermittent wifi issue when I am on my home network, and up to now, I did not have the same issue with other routers (but I did not have the opportunity many other routers, and the ones I used where not used during a very long time). If the type of router or the router config plays a role, it might be interesting to know, from a troubleshooting perspective.
But again, in my case, other machines (Iphone, Windows PC, Linux PC, Ipod, another MBA from 2011, a Macbook pro) work very wel my home network, while my brand new MBA 13 " I7 512 G 8G Ram erratically loses the connection and refuses to reconnect. So, even if I would be able to fix the issue at router level, this would not mean that I would not have the issue with other routers when "on the go". And I do not expect every router administrator to kindly tweak their infrastructure in order to accomodate the MBA mid 2013 Apple happens to put on the market!.
In my opinion, fixing the issue at router level would just be a temporary local work around, but would hide the very core of the problem: apparently, at least some new MBA do not work properly with infrastructure that works perfectly with most other devices. And that is not acceptable.
Let's also put it bluntly. In the ITC world, this is an old trick of many manufacturers to blame external causes, not their product. It is allways the other products that cause problems! Apple is certainly no exception here.
As agreed with Applecare, I still have to let my MBA hardware tested at the local authorized reseller, I just need time to do that, after all, I bought this machine because I needed it! Anyway, I do not expect many results, as the issue is intermittent, and might not occur on every router!
I am really deeply disappointed by this new machine, and as a result, by Apple as a whole. I entered the Apple "ecosystem" a couple of years ago, and I start wondering if I did not make a very big mistake. I am considering what it would take to gradually drop Apple altogether, I mean Iphone, Macbook airs & pro, iTunes, iCloud, iMatch, everything! Not an easy one. Apple is good at hooking us, but leaves us in the dark when problems arise!