I've recently rented this place for 4 days with wifi listed as an amenity, and have had continuous problems with the wifi. I've contacted host who's actually been pretty responsive, and found out that the same wifi is actually shared among with other places. For me internet = work, and no connection = loss of income. Also, another thing which I didn't like in this particular case is that the owner kept telling me "she can't do anything about it", instead of providing an alternative solution.
Anyway, I survived somehow, but the question now is, can you provide me partial refund.