I think it could be a ownership permissions problem, or maybe "gksudo" got uninstalled or is not working. I think it would be the first problem though (ownership permissions).
Nothing inside your personal home folder should by owned by anyone but you (your username), so not even "root" should own your files. You can you check the permissions of files and folders in your home folder by using the following command in the terminal:
If the command returns "yourusername yourusername" (jake jake) then ownerships are fine.
find -printf '%u %g\n' | sort | uniq
But if the command returns "root root" or anything other than your username, then you will need to regain ownership of those files. The following command will use chown to change ownership of all files and folders recursively inside your home folder.
(replace jake with your actual Xubuntu username.)
sudo chown -R jake:jake /home/jake
Now try running Synaptic again from the start menu, or with the command "gksudo synaptic".
Also, using the "sudo" command with graphical applications can mess up permissions settings pretty bad in some cases. It is always best practice to open graphical applications with gksudo instead.
You should never use normal sudo to start graphical applications as Root. You should use gksudo (kdesudo on Kubuntu) to run such programs. gksudo sets HOME=~root, and copies .Xauthority to a tmp directory. This prevents files in your home directory becoming owned by Root. (AFAICT, this is all that's special about the environment of the started process with gksudo vs. sudo).
Hope this helps.