If you have a private key you wish to keep safe (I'll call it Key A, which could also be a collection of private keys tarred together into one file to keep safe), create another public/private key pair (Key B).
Securely copy Key B around to multiple computers that you trust. This can be done by creating a temporary public/private key pair (Key C) on the destination computer, transfer the Public Key C to the original computer, encrypt Private Key B with Public Key C, and transfer the encrypted file back to the destination computer where Private Key C can decrypt it.
With Private Key B on several machines you trust, encrypt Private Key A with Public Key B, and place that file in secure storage (could be on a location you don't trust, like Dropbox).
So, then if ever Key A gets lost/corrupted on your local workstation, it's an easy/quick restore to grab the Key-B-encrypted-Key-A file from Dropbox and decrypt it to restore.
If Key B gets lost/corrupted, you still have Key A, so you could just create a new Key D to replace Key B and do the setup again, or go grab a copy of Key B off one of the other computers you trust you made copies of it on.
If your whole computer is lost (you lose Key A and Key B at the same time), you will need to go to one of the other computers with Key B on it and grab the Key-B-encrypted-Key-A file from Dropbox and decrypt it to restore Key A.
So, this plan allows Key A to be kept safe using traditional backup options copying the file to many (possibly untrusted) locations, which opens up offsite, offshore, and off-planet options. It also means Key A can be restored quickly if need be, as the Key-B-encrypted-Key-A file can be passed around untrusted, so can be attached to emails or whatnot.
It keeps Key B safe by being on multiple trusted locations. This being ServerFault and not SuperUser, we're likely talking in a corporate setting, so hopefully the corporation has local servers and co-located servers they trust that can host such things. In addition to live, running servers, copies of Key B can be put on offline storage (tape backups, archival CD, etc.) in a bank vault or similar. Restoring Key B then becomes a slower process as you may have to visit the bank vault to go get a copy, and you should be checking those offline backups periodically, so you can catch the situation like the original post where the CD went bad.