To me, the word "anymore" doesn't sound right unless there's a negation. "We don't do that anymore." "It's not here anymore." "I can't remember anymore."
However, I have noticed that it's becoming increasingly popular for people to use "anymore" with statements that aren't exactly negations, like your example. The implied meaning of "how often do we get this anymore?" is that we DON'T get it (very often) anymore, but the speaker doesn't actually use the word "don't." The negation is merely implied.
Some people will also ask questions like, "Do you ever go there anymore?" or "Can you buy these anymore?" The implication is that the speaker thinks the answer is probably no.
As Miss Alexis says, though, this usage is somewhat informal. To me, "anymore" without a negation always sounds very strange (the first time I heard it, I actually thought the person who said it might not be a native English speaker). I think this usage is more popular in some regions of the US than others, which may be why I'm not used to hearing it.