I'm sure Bri's gonna move this to 'Remote Power' shortly. In before the move.
Firstly, you've got an External Battery and not a Battery Box - a battery box is used to power mics.
Secondly, here's what your technical specs say about your product:
•Samsung Grade A cell and premium microchips ensure high quality batteries; Premium aluminum case provides enhanced protection; Secured battery safety with 4 layers of smart safety protection circuit; Advanced power lock technology with standby time up to 6 months after fully charged. 500+ recharge cycles over the life of the battery.
Seeing that you can probably get 10-12 hours out of it, I wouldn't charge it again just yet. Since it can hold its juice for up to 6 months, I'd say you're safe to just keep it aside and not power it up/charge it.
There should be no battery effect.
Swap out depends on how many times a year you plan on charging it. It also says 500+ recharge cycles so you could - in theory - recharge it daily for the next year and a half if you felt so inclined.