The front wheel rim thickness on my fixed varies between 1.5 and 1.25 mm. It looks like it will be OK for the rest of this winter but it'll need changing before I use it next winter, I'll be keeping an eye on it for now.
I am quite encouraged by this thread. I have never worn through a rim, being a bit on the heavy side, I am much more used to cracking rims between spoke holes. I do, though, have a pair of "tough as old boots" Campagnolo Sciroccos, which are getting spectacularly concave, on one of my winter Bianchis. I think I will keep riding them till they go in holes!