Ring doorbell 2 battery runs down even though hard wired

I have a Ring Video Doorbell 2. I installed it at least a year ago - hard wired to where the existing doorbell had been wired. It shows up as hard wired in the app, and it rings the old doorbell chimes when the button is pushed. Recently, I discovered that the battery was run down and the doorbell no longer functioned. I assume that the battery is normally continually recharged by being hard wired. I removed the battery and recharged it, and the doorbell started to work again. But the battery is rapidly discharging, so whatever circuit originally recharged it must no longer be working. What can I do? I am not prepared to continually remove/recharge the battery. The thought of having to buy a new doorbell does not excite me - and any replacement would not likely be a Ring.