The BitsyXB manual calls for an external battery to hold the RTC. The personality board has a battery but does not seem to have a charging circuit for it.
Does the BitsyXB supply the charge or are you suggesting just having a long life battery with no charger?
The RTC backup circuit uses so little current (300 nA typ; ref section 6.3.4 of BitsyXb user manual) that battery life is determined not by capacity but by shelf life. Use a lithium battery for this application. No charging is necessary.