Kate's Hair Color - LOST ?

I am re-watching all of the LOST episodes. I've been trying pay closer attention to detail. Just now, while watching episode 22 season 1 "Born to Run", I realized that Kate is not naturally brunette. The episodes clearly indicates she was blonde and dyed her hair brunette since she was on the run. SO! Why doesn't Kate's hair grow out into blonde while she's on the island? It must grow, but there is no indication her hair was ever dyed. WHY IS THIS? And why can't I find any forums or anything already posted on this topic?? HELP!!