Perhaps the problem is with the battery contacts in the phone? If the battery is not quite making a proper connection I could see it leading to random reboots and turning off - also problems charging and maybe even other random issues.
It might also explain the battery level seeming to suddenly have gone lower - bad contact/increased contact resistance could mean the phone sees a lower voltage than the battery is actually charged to.
I’d try cleaning the battery contacts in the phone with something (ideally IPA), or maybe try inserting a piece of paper between the bottom of the battery (i.e. opposite end to where the contacts are) and the phone to increase the contact pressure. If that solves the problem, a permanent fix could be to bend the contacts outwards slightly.
Some FP2s are susceptible to bad battery contact. See this thread: