iPhone 6s incoming calls won't start when Apple headphones are connected
You absolutely will want to do some tests or work with AppleCare / support on this. I get the same very seldom, and if yours happens each / every time your diagnostic logs could let Apple fix this for everyone (assuming there are bugs in the code on answering calls). 

Almost certainly not battery, but it could be. 

I would make a full backup then try in order:


Reset network settings and test. 
Make final backup then don't backup next steps. 
Erase phone, set up as new and test. 
Erase again, restore final backup and test. 
Don't forget to set up backups again.