Since my Touch ID has been working great since I last deleted and patiently/diligently re-registered my digits, I'll make one final post...
The registration scans done carefully appear to be critical to long-term successful scanning, perhaps even more particularly with worn hands. Therefore, I believe that rushing through and/or a lack of detailed attention and care taken while registering...is the enemy.
So, here are my final observations:
1. Again, I don't think this is a major issue since there's just not enough complaint here or on the wider Internet to suggest it is.
2. Take your time. Sit down and calmly go through the registration procedure. Rushing will not help.
2. Make sure your hands and the sensor are clean. If you wash your hands before beginning, which might be a good idea, make sure to allow ample time (perhaps 10 minutes or so) for your hands to completely dry. The sensor definitely doesn't seem to like wet digits. And do not use any solvent to clean the screen or sensor—use a soft, lint-free and dry lens cloth (a microfiber lens cloth works well). And although some use a very slightly moistened lens cloth (distilled water) for the glass expanse when really filthy, I would suggest not when cleaning the Touch ID sensor/Home Button because it's a place where water is more likely to penetrate to where you don't want it.
3. When starting each registration, present the finger pad CENTER not the edge or butt (thumbs, give it the pad center of the top half) and then lift and place -in position- (don't move much laterally). Only when requested by the procedure do you reposition and present edges.
4. When registering, pay strict attention to the written instructions and particularly the images shown.
5. If you continue to have problems after perhaps a half dozen registration attempts, collect all your troubleshooing data and contact Apple directly, either via AppleCare or by setting up a Genius Bar appointment. Don't just wait around hoping that Apple will issue a fix of some kind, as there may be none coming. Take direct action with Apple to get your problem resolved.
Best of luck.