My wireless anemometer unit suffered from a failure during some intense cold in January 2010, it turned out to be the supercap, however I think it was just coincidence. My main unit is older and has not suffered from this problem. I purchased two replacement caps and a friend kindly removed the faulty one and soldered the new one, been fine since - at least if the other fails I have a spare. I thought Davis had sorted this, as yours is newer I'm surprised, although it may not be this which is the problem.
If you open the unit up, the supercap is seated under a white plastic box which I think you unscrew, mine had leaked which I guess lead to it failing. Replacing the main battery didn't work, although during daylight hours it did come back to life temporarily - I have no idea why!
I may have some pics somewhere...I'll have a dig.
This post has been edited by Jute: 03 February 2012 - 22:35