Well, I guess that if you told an Italian person that Andrea should be unisex s/he would also say it's strictly masculine. I'm Scandinavian so that might be the reason why I can't see August as a a unisex name.
But I never said that August can't be used as a girl name in English speaking countries but I understand people who say it's a masculine name. In my first reply I simply tried to explain why some might see it as strictly male (as you said that you couldn't see how it is strictly male) and I think my Japanese name example is a good explanation for how some feel about August.
I can't really argue against the whole month name thing. I tried to come up with a consistent theory of use and origin but failed ;) But according to the database May derivs from Maia, a Roman goddess and not from Maius (I wonder which is correct...)