Apple Pencil 2 flat battery?

Hello,

I’ve been having an issue with my Apple Pencil, second generation. I always leave it docked on my iPad Pro 11-inch. Sometimes (more often than not), when I pick up my iPad and “unplug” my pencil to use it, it only works for a few minutes before showing 0% battery. After which I have to charge it again, even though I always leave it charging. Does it stop charging at some point and just starts draining its own battery? Should i get it replaced or is there anything I can do? I’ve had it for a few months only, and I’m not sure how I could’ve damaged it.