You should know that making eye contact in Japan is not normal even for Japanese people. Of all the things you're worried about, don't let that be it. I've experienced this too, but man, it will only bother you if you let it. I work with Japanese people everyday and not the majority of them do what you describe. I've also lived here for 3 years, not just three months. Fact of the matter is, anywhere here in Japan, some people aren't comfortable around foreigners or have had bad experiences with them. On the other end of the spectrum, haven't you had someone come up and try to talk to you yet? young or old? In english or Japanese? This does happen to, and its awesome when it does.

Again, just don't let it get to you. It does not make the Japanese any less respectful of others.