I've had a couple issues with Touch ID. I checked on Apple's website and they had a few suggestions. When I first got it I picked 5 fingers and learned each one (which is the limit). Apple states if you have multiple fingers learned it can slightly delay the response time.
What I found was I actually only ever used my thumb as I always use my phone in the same hand. So I unlearned all fingers and only used my thumb. Since then it's worked almost 100%. The odd time it doesn't is when I'm at work and have dirty fingers. I also cut my thumb and while it was healing it didn't work very well either.
So now I learned my thumb and one more finger as backup, and since they are completely different "types" of patterns the response time is still great. Apple also states that if you have "similar" prints it can delay response.
I'd have to say that Touch ID is very reliable, and if you apply a little common sense to what's actually going on (like me switching to my finger while my thumb was healing) it works great.
I have to wonder, how many other people learned 5 fingers "just because"?