This is probably going to be a very silly question, but someone's got to ask it...
You've got the wiper switch in the right position, I assume (one up from the OFF position) and the frequency/sensitivity adjustment (on top of the switch) set towards the right? It doesn't have to be all the way over but it might be too far to the left to operate unless it's absolutely pissing down.
EDIT: It's also worth mentioning that poor light conditions make the rain-sensor less sensitive - I find that quite annoying sometimes and have to revert to manual control. This happened on my previous (Jaguar) car as well as the current Q3.
Those auto wipers also operate sometimes for no reason. ie bright sunny day, and not at all sometimes in the rain. Q3 is my 4th car with them (2 Mercs & 1 Audi previously) and I reckon the idea is stil in its infancy. No doubt system control will improve in the years to come.