No VP loophole

American Presidents cannot serve more than two terms. 

The 'VP loophole' is to avoid this constitutional restriction: become Vice-President, have the President resign, and then the VP becomes the President for the third time.

Unworkable

To serve as VP, the consititution requires that person to be qualified for the office of President. 
      
Having done two terms disqualifies a person from being President again. 
      
So serving two terms as President likewise disqualifies a person from serving as VP. 

As they can't be VP, then there is no 'VP Loophole' to become President with.

So can this 'loophole' even be called a loophole if it cannot fulfil its express purpose? 

Origins

A President removed from office (resignation, death, impeachment) is succeeded by their Vice-President.

This does not count as a presidential term for the now-President because they are serving out the term of the elected President. (As long as it's less than two years, according to the Twenty-second Ammendment.)

So a successor President who's not won a presidential election is still eligible to win, and hence serve, two more presidential terms. (Or win and serve one more if they've done one already.) 

Nonexistence

A two-term President isn't viable for the office of President again, meaning they are also unqualified for VP. 

As such an individual can't be VP, they can't use the 'Loophole' for a third term. 

But the 'Loophole' is specifically to give someone a third term: as it cannot give a third term, it doesn't exist!