You can save event clips, however, I don't think you can save video that is not an event. I believe that is true for cameras in the Home app, in the Nest app (with compatible devices) it is different.
To save an event clip, go to the event (either scroll to an event or go to full history), tap on the 3 dot icon, and then "Save clip to device."
I apologize for my late response and thank you for all of your patience while waiting for a reply. I can definitely understand how frustrating your situation must be, but I wanted to make sure that your issue was addressed. Do you still need help with this issue? I know that there's been a delay in response since you posted.
Please let me know if you need further assistance.