Independence is totally cool, and you've got to let a girl do her own thing. She's got things she likes to do that you don't, and if it makes her happy, set her free. It'll be good for you too, because a happy and independent woman is a woman that's easy to love. At the same time, though, you've got to watch out for some very specific warning signs.
If she doesn't even tell you where she's going anymore, and doesn't tell you about it when she comes back, that's not good. If you haven't seen her in a couple of days and it doesn't even seem like she missed you, that's not good. If she's out all the time with "friends", and you can't seem to find any time to spend with her alone, then that's definitely not good.