outdoor camera battery immediately discharging

(First, I wrote this whole post, my first, then went to post and it presented a popup for me to create a posting account. I did this, and it reloaded and lost my whole post. Not a great first impression.)

I have had two outdoor cameras, both with solar panels, for close to a year. 

Last week, both showed unavailable, which eventually required removing and re-adding them to the system. 

This worked for one of the cameras, but the other one never shows a flashing light, despite fully charging the battery externally, pressing the reset button, or holding the reset button for 16 seconds as described at https://support.simplisafe.com/conversations/cameras/outdoor-camera-battery/637caa679c580606e77e3412

Even when I charge the battery for 2 days or more with USB (it goes from 1 blinking dot to 3 solid dots), as soon as I put it in the camera, I get the chime, but never any light. I remove it and immediately go to recharge it and it again already shows one blinking dot. 

Do I need a new battery?