Well, I'm not actually running Mint anywhere at the moment. I''m using Aptosid, but if both Aptosid and LMDE (I don't care about Ubuntu or anything based on it) disappeared, I would switch to another Debian Testing/Unstable-based distrio such as AntiX or do a netinstall of the Xfce edition of Debian Testing.
If the Debian Testing and Unstable repositories (along with all of the distros based on Testing and Unstable) disappeared, I would probably give OpenSUSE Tumbleweed a try, being the only other major rolling-release distro to use package signing (guess why I am not using the otherwise-great Arch Linux, and it's unclear if PCLinuxOS uses it, despite the use of apt).
If I didn't like that, I would probably give Gentoo a try. I have always wanted to try a source-based distro, but the compile times are off-putting, so if I did try it, it would probably be for the long haul because of that.
These choices are made based off the 3 most important things a distro should have for me - a rolling-release cycle, good, sensible, security-related choices (package signing or some other form of package security, not logging in as root by default etc.) and a wide selection of packages to install in the main repository.
I can change everything else myself. The three things I mentioned above are the only things that can't be changed by the user, hence why they are the most important points for me.