Prevent Vim from clearing the clipboard on exit
Synthesizing answers from superuser, just add the following to your .vimrc
autocmd VimLeave * call system("xsel -ib", getreg('+'))
Install Parcellite, or glipper for Gnome and klipper for KDE.
Restart your computer or run it manually.
see: https://wiki.ubuntu.com/ClipboardPersistence