Three Term Vice President

[Never]

It's definitely an interesting scenario. I think for that to happen, it would require an popular established (likely elderly) vice president who didn't have much ambition, and a younger president from the same party who wanted to have close advisors with a significant degree of relevant experience. Except for the political party aspect, this case would probably be similar to how President Obama retained Secretary of Defense Robert Gates as a means of continuity. On that note, perhaps we would be more likely to see a three term vice president during wartime, with the new president preferring to keep someone who already has a solid grasp of the detailed operations of the war.