I think part of the issue has been that the position of Vice-President hasn't been taken too seriously until relatively recently. I mean, the VP wasn't even the assumed successor in the next election until 1960-ish. (Except for Roosevelt/Truman, but then again those were special circumstances.) Wasn't part of the reason why Wilson didn't resign after his stroke because the general attitude was "Who the fuck is Thomas Marshall?"
Have no tradition of term limits. The reason why British PMs resign is because they can keep getting re-elected indefinitely, and many don't want to.
I can't come up with anything that's not going to be called ASB.
Nixon resigned over Watergate, then Reagan resigns over Iran-Contra, Clinton resigns over Monica. By the time Bush enters office (or Gore?) it's seen that no president has peacefully left office after two full terms since Wilson.
Of course, butterflies from B should affect A to a point, so...
What about Ike?