There are basically two possibilities. One is that he likes you and he's so nervous when he's around you that he's staying away just to avoid the distraction. He may have picked up on your looking at him and not known what to do about it. Unless he's a complete idiot, the thought will have occurred that a girl is staring at him because she's attracted to him.
That's a nice thought, but there's also the possibility that what this guy has is not AS, but actually some kind of paranoia or schizophrenia, which has symptoms that can look like AS superficially, especially when one is doing the sort of wishful thinking one does when attracted to someone.
You need to figure out which it is. The only way to do that is to just talk to him. If he's attracted to you and nervous, he may blush or stumble over his words, or fidget nervously, or start rocking, etc. If he's paranoid, he'll probably be very calm and give curt, short replies which are supposed to make you go away or ask questions about why you're watching him or what you're doing following him, depending on how severe his paranoia might be. If he does that, it probably IS best you avoid the guy.
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Self-Diagnosed Dec. 2010
135 Aspie, 65 NT--Aspie Quiz
AQ 40
BAPD--124 aloof, 88 rigid, 83 pragmatic
EQ/SQ--21/78--Extreme systematizing