keypad

@rkviklys suggest you forget about rechargeable batteries and call SS to troubleshoot and or replace your keypad. Either it is too far from the base (unlikely) or there is interference (More likely) or the unit itself , is defective.  My batteries last at least 8 months.  Try moving the base, if no improvement, then the keypad.  Again, I would call SS to troubleshoot.

By default the keypads will wake up when you get close to them and the display will turn on. If your keypad is constantly waking up, like non-stop (which is a thing I've seen reported once or twice) then your batteries could be depleted quite quickly. You can turn this off in keypad settings menu by change the value of "power savings" to "on".

FYI, I think the keypad uses the same technology as the motion detectors to detect movement (but less powerful and with a shorter range I suspect?) which is a PIR or Passive InfraRed sensor. These sensors detect changes in the amount of infrared radiation impinging on them so constant changes in the infrared radiation levels could cause this behavior. (Or as captain11 suggested, the keypad may just be defective or broken.)

I'd try a fresh set of batteries and enable power save to see if that helps. I don't think it's the most likely cause but it's definitely a possibility.