Whether or not the battery meter is inaccurate, if the device drains it's battery past the time it can initiate a graceful shutdown, it is malfunctioning.
That being said, the reboots might be exposing some database error/corruption that has never been properly fixed. In the Kobo settings, it would be worthwhile to "Log Out" of the kobo account to clean out and refresh a new database. (Note, this will loose all current reading progress and annotations for sideloaded content.).
I would also add, if you are draining batteries to the very limit on purpose due to some old, very very outdated advice that you need to treat rechargeable batteries that way... pls stop doing so. It can still be helpful to calibrate battery meters this way, but it is in no way better for the battery.
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