A couple things OP:
(1) When you go through the setup, lay your thumb flat through the first round of scans. Move it around, try different angles. Don't just set your thumb in the same spot each time. You need to let it read your thumb (or whatever finger) from various angles. On the second go round, when it reads the edges, be extreme with it. Use the sides of your thumb and again, let it scan your whole thumb.
(2) The scanner gets better over time. Re-doing all your scans the second it doesn't work won't make things better. When I first set it up it failed once or twice. Now it works flawlessly. I continues to learn as you use it.
(3) Make sure you are on iOS 7.0.1. Seems like people are here complaining about issues but aren't on the latest release that Apple pushed out to fix some bugs in the 5S and 5C.