I had similar issue with the ios 10 on iphone 6. It was working fine until I update to ios 10. Phone stopped holding charge and touch id stopped functioning.
I did restore to older version. Format and configure as new phone still no issue.
Couple od frens from US got it repaired for free but now that I am in India I went to local service center and they ask me to pay Rs22k for replacement of phone to new phone which has 3 months warranty and that device not allowed to buy applecare. Wahh thats gr8.
Before this discussion they run diagnostics and detect touch id hardware issue. Which is strange after ios 10 installation appeared. I believe Ios has broke the hardware and brick touch id and now apple is asking for money to replace phone.
This is amazing and wonderful service.
I believe its the case with everyone and ur not getting support from apple for their ios version release and manufacturing ic issue.
I am not sure about how and when apple is gng to fix it but I have blocked ios update on my other phone 6s plus and kept it to 10.0.1 which is stable and not having any known issues.
Guys we all need to create blog and write our grievances and run a campaign against apple for their so called release issue with some iphone hardwares which they manufactured.
What say...
Hoping apple look into this issue and fixes it on topmost priority.