Sometimes, depending on the guy, it is really hard to tell if he is losing interest or not. A lot of girls, me included, think he is just busy with work/school or even simply playing a bit hard to get (because guys do it too sometimes). Once we realize that he has truly backed away, I think most girls do, or at least should, do the same.
Because they don't want him to... I've learned that chasing a guy when he's losing interest is a losing battle. I've done it one too many times and I've learned my lesson. I've also learned that chasing a guy who has already made his mind up is a horrible idea. You can't change their mind so don't try. I learned that the hard way.