It sounds like you would benefit from re-registering your fingerprints. When you did the process originally, did you shift your finger around each time it asked you to lift up? When I registered my fingers I would rotate them slightly each time, occasionally shifting my finger up or down over the button, and I even pressed down with the tip of my thumb. It's extremely rare that I need to press my finger down a second time because it didn't take the first; I probably go for days before experiencing one event like that. It seems most people who experience frequent rejections just lift up and put their finger down, over and over with very little variation.
As for TouchID not adding security if someone knows your passcode... that's true, but consider this: every time you type in your passcode, someone could note what you're typing in and memorize your passcode that way. If you use TouchID, there's no chance for them to get at your passcode. You can also make your passcode obscenely long, since you'd only need to type it in after restarting the device. It's a far more secure and convenient option than the passcode you're likely to use without it.
