The answer given above does work:
sudo apt-get install software-center repairs this. However, the questioner asks: how can one avoid this issue in the future?
It seems that during installation process, the Software Center may actually uninstall itself -- without giving a clear warning about this. This, then, is a challenge for a future Ubuntu -- that the Software Center is able to give a clear indication whenever key software is about being uninstalled. Here is an example of how it can happen, and by being aware of this issue, one may avoid it. It applies to Ubuntu 64-bit 13.10, at least, and I haven't seen the same for Ubuntu 32-bit.
When you start Wine in Ubuntu 64-bit 13.10, it complains about lack of a proper p11-kit. If you use the Ubuntu Software Center to find a different p11-kit, more suitable for Wine, and install this, out goes the standard p11-kit that it seems that the Ubuntu Software Center itself is using. Thereby, for consistency, the Ubuntu Software Center efficiently uninstalls itself. By re-installing the Ubuntu Software Center, it will switch back the p11-kit. (This is something that only arises if you click on 'Show technical items' and click ahead eagerly.)
But the fact that askubuntu.com can search up and answer this question so readily when I needed it shows that askubuntu.com is working really well! :-) Aristo T.