Is it because you want to avoid her, think she's attractive, or what? I see lots of guys look at me and they always look away. And is the reason the same if you are a very attractive guy compared to a lesser attractive guy and if its a very attractive girl or a lesser attractive girl?
I don't think it has much to do with the relative attractiveness of the guy and girl. The reason is pretty much the same, which is that the guy is worried about creeping you out if he just keeps looking at you. And he probably doesn't want to make it too obvious to everyone else either.
Insecure, shy, submissive, scared, or not interested.
To the guys answering because you like her. How do you know she is interested in you? You don't.
Here is an idea, make direct eye contact, smile (Just a tip, you smiling at her increases the chance she will smile at you), and wait for her to break eye contact. She looks down (virtually assured if she smiles back.), you go talk to her if you want to.
She is staring? The longer she takes to break eye contact, she is literally creating a stronger emotional bond to you. It does not get any easier than her doing the work for you. Feel uncomfortable all you want (knowing she is feeling better and better about you the longer it is, why would you feel uncomfortable? You should be more confident knowing she is making no bones about being interested in you.), but DO NOT break eye contact first.
It is creepy to them when they break eye contact and you continue to stand there looking at them afterwords. Start walking towards her to go meet her, or walk away. Pick one, your choice. If she looks down she will at least talk to you as long as the first thing out of your mouth does not fire a bullet into your foot.