Well technically you can back up to the likes of a DVD recorder via SCART but its in SD and takes as long as watching the programs, so that qualifies as No in my book.
VM should make TiVo's functionality clearer IMHO, its specifically designed NOT to let you back up or even store programs for long periods of time. Its really a "time shifting" device, you record something to watch at your convenience.
Archiving or saving up to binge watch a season of a particular show (as a lot of people want to do now) is NOT what it is good at.
Welcome to the Community, I'm sorry to learn about the problems you're experiencing with your TiVo service at the moment.
I'd like to run some tests on the set top box from our end but I've not been able to locate your account unfortunately, so I'm able to do that would you be able to respond to the private message I've sent with the requested information?
You can view the message by clicking the purple envelope on the top right of this page. I understand that you don't want an engineer to come and take a closer look while you've got programs to get through, so I won't arrange for action to be taken, I'll just take a look and let you know.