I’m having the exact same problem.
In fact, I have two sites that mirror each other in every way (theme, plugins, structure, content) with the exception of language. One is fine, the other keeps on asking me to update to 3.7.1, even though it’s already 3.7.1. But when I go into the update tab, the request to update disappears.
Switching to another theme is not an option for me, as too much of the website functionality is tied to the theme (Headway 2.0.15.) I just can’t afford losing it all.