First Generation Sensor-Critical Connection Error and Cannot Remove

Two of my first-generation contact sensors stopped working. I suspected a dead battery, but since the device did not register on the system, I could not determine the battery status. First I tried resetting, then removing and re-adding, but nothing worked. Then I tried a new battery and added the device back, and all seemed to be OK until a few days later when I noticed it was returning a "critical connection error" message in the app. I read one of the posts on the subject here and tried everything -- resetting, removing, etc. The app will not allow me to remove the device. It fails every time I try ("we had problems communicating with your device") -- both before resetting and after. This is very frustrating. How can I get these devices up and running again?