I would keep a backup image on an external drive, preferably 2 external drives, to avoid the situation you've described - as you say, if there's an issue with the drive in the machine it's unlikely you'll be able to use the recovery media stored on that drive.
Personally I have an external drive by my PC and my gf has an external drive in the other room, every 4-6 weeks I image my PC to my drive, she images her laptop to her drive, then we swap, so both drives have a reasonably up to date image of both machines.