Usually within a week. Are you trying to get upgraded?

FYI, the JW San Antonio is very nice! I stayed last weekend and they upgraded me to a King Suite (I think that was what it was called). You get two free drinks on your first night, so make sure you take advantage of that before the lobby bar closes at 11.

Also you might be able to use your annual free night certificate at that hotel -- not sure what the category goes up to, but I think it's a Cat 5 and that makes this hotel eligible.