Howdy:
Finding the root cause will be tricky. When the display on the DECT phone says that, it means that the phone is detecting that it has lost the on-hook voltage from the phone line. This can happen when you reboot the OBi device (press **9 then 1 on your phone's keypad to observe this), or if there is a hardware failure with the OBi or the phone. Your test with a corded phone doesn't prove much, since it doesn't have a display to give you that piece of information.
Two guesses:
First, the OBi device, or its power "wall wart" adapter could be going bad. It could even be as simple as the socket into which the wall wart is plugged could be loose (metal fatigue in the springy contacts). The adapters do go bad, and fortunately, you can buy a new one as a cheap test:
https://www.amazon.com/gp/product/B07HNL5D56. Of course, the entire device could also be going bad.
Second: your cordless phone's base station and/or its own wall wart could also be going bad.
Less likely, but still possible: you could have a firmware or configuration error on your OBi that is sending it into a reboot condition. You could delete it from the OBiTALK dashboard, then do a factory defaults restore (press ***8 then 1), then re-add it to the dashboard and set up your service providers again.