Are you relaxed or natural?
I know that it can be little frustrating having twists with relaxed hair, cuz the shorter pieces tend to stick out. I suggest just re-braiding with a little bit of moisturizer in your hair and the fake hair so that it "holds" better. Other than that, there really wasn't any why I was able to prevent it from happening to me.
I don't think it will damage your ends though, as long as you treat your twists as your real hair, you should be ok.