Have you...
Caused scratches on your fingerprint scanner?
Cleaned the scanner thoroughly?
Wiped your finger from any oils?
Is your phone a 5 or a 6?
I have the iPhone 6s and due to the way I use my phone, I usually press the home button to activate it. When I press the button, my finger triggers the finger scanner quicker than I can even take my finger off the button. I think my scanner works too good sometimes when I want to just look at my lock screen to either check the time or see what song is playing.
However, back on my 5s, it would take a second or two, or some readjusting to get it to work.