Here’s a list of the losing VP candidate over the past couple of decades, going backwards from the last election:
Ryan, Palin, Edwards, Lieberman, Kemp, Quayle (incumbent), Bentsen, Ferraro, Mondale (incumbent).
Out of this group, only Lloyd Bentsen (who subsequently became Treasury Secretary), and Sen. Joe Lieberman and Rep. Paul Ryan - have had held public office post-election.