Get in touch with htc they will replace the battery and fix the phone free of charge normally. I have had good experience with their support in the past.
I think the battery thing might be something to do with Lollipop but can't pin it down. The phone's already been back once for the sim card problem and they didn't do a great job plus a friend's just had his Desire Eye back and they totally failed to fix the fault on that. I think it's quite hit or miss if you get good service or not.