A couple of thoughts on this issue:
I have an 2GHz/8GB/256GB/11" Air and like many people had the issue with crashing when running google crome, I stopped using crome until it was updated and had a few minor remaining issues that seem to have been resolved with the last two updates.
I use my Air heavily for software development wtih java, eclipse, solr, mongodb running all the time. I also use part time for video and image editing with Apple tools and Photoshop as welll as the usual email, web, and social uses. It is more stable than my old air was under lion now with weeks between hangs (althought not back to a snow leopard never ever crash level of stability).
As I understand it, the crome related crashes were because crome triggered a specific bug in the video driver. It is possible that other applications can trigger similar bugs. If you did an upgrade install you may have an old driver or corrupted config file. If you don't see any software association with the crashes and running some specific piece of software and you are sure you have a clean OS install - it is likely a hardware issue. Remember the new Air has a new cpu, chip set, and graphics chip and the associated drivers will be new as well, so there are bugs and your specific hardware may be marginal and more apt to trigger them.
Crashes every few hours are intollerable. I'd suggest taking a copy of your system logs showing the crashes every few hours to the Apple Store and politely asking them to fix it or give you a machine that works.
Best wishes, this is one sweet machine, when you have a good one.