My siblings and I are getting this mailbox printer for our Mom for Mother's Day, so this will be new for us. What about just unplugging the phone jack/electric cord when your mom isn't at home, eg vacation, hospitalization, etc. Then when back at home, plug back in. I suppose you might still get all the previously undelivered emails and there would be lots of them. But at least the machine wouldn't be running when no one is at home, reducing the worry of some electrical malfunction.
I realize this doesn't help with "using up" your subscription time, and it would certainly be nice to suspend it when necessary, just like you can with your newspaper subscription when you're going to be away from home awhile & they just tack on those unused days to extend the expiration date.