I've the Thunderbolt Display and a late 2011 MBP and am having no problems. I've two USB devices connected to the 'hub', four external FireWire 800 drives, etc.
You need to call AppleCare - there are a handful of people who have mentioned problems with the MBA and the Thunderbolt Display here. Try a search and see if anyone has come up with a solution. You may have to lug your Display and MBA to your local Apple Store or an AASP and have them look at it.
Good luck - sorry that you're having problems: my display and MBP get along just fine...