Could be several reasons, but the most common one is, hands down, because the guy realizes that this girl isn't going to sleep with him.
Most guys these days only approach girls with the hopes that the girl will eventually sleep with him. Of course, this doesn't always happen, but because this is the only reason he even started talking to the girl, if after a few days he gets the feeling that this girl isn't going to waste her time witha scumbag like him, he'll stop talking to the girl.
It's not called "losing interest", because the interest was never there to begin with. The only thing a lot of guys want, is sex. So it doesn't matter if the girl is clingy, boring, annoying, interesting, funny, smart, or whatever. The only thing that matters is if the girl sleeps with the guy or not.
And this is why, when the girl then asks him why he stopped talking to her, he doesn't tell her. Because he doesn't want to admit that it's because the only thing he was after, was sex.
Because if we really care about someone, we don't just stop talking to them. We TELL them! If she's clingy, then we tell her we need some space. If she's boring, then we MAKE her interesting! If she's annoying, then we tell her how her actions are affecting other people. Unless she's dumb, and doesn't understand that we're trying to help her, we're not gonna just give up and stop.
But like I said, not all guys are like that. Some guys are just after sex. Good luck trying to find someone who actually cares enough about you that he will stay with you even if you don't have sex with him immediately. Because it's come to my attention that girls aren't attracted to guys like that. =)