At Volokh Conspiracy, a group blog run by mostly conservative law professors, blogger Ilya Somin writes [emphasis added]:

Conservative critics of Elena Kagan, such as William Kristol and Ed Whelan, have focused on her role in trying to prevent military recruiters from interviewing at the Harvard Law School campus because of the law banning openly gay individuals from serving in the military. The critics argue that Kagan's stance was badly misguided and a possible indication of anti-military bias. I think this critique of Kagan is half-right. She did make the wrong call, but there is no proof that it was caused by anti-military bias.

I've been scratching my head over the same point for days now, as the right-wing media desperately bang the drums and try to turn the military recruiting issue into a Thing. What's confusing is the attempt by Kagan's critics to take the very narrow issue of on-campus military recruiting during the “Don't Ask Don't Tell” era, and extrapolating from that some sort of burning hatred for the military on the part of Kagan.

As Ilya Somin, a George Mason University Law School professor, points out, Kagan in this case was responding to a very specific military policy which affected campus recruiting. And as the blogger notes, there are no other documented examples of Kagan somehow thrashing out against the military. (In fact, it's just the opposite.) Meaning, there's no evidence that this was part of any larger trend:

In sum, Kagan's support of a ban on military recruiters is legitimately subject to severe criticism. Senators should certainly question her about it. But I don't see any reason to believe that it reflects a general hostility towards the armed forces.