1997: Person A is elected President
1998: Person B is elected President
1999: Person B is re-elected President
In 1998, Person A is clearly the Immediate Past President. However, what happens in 1999? Some members are certain that Person A should stay on the Board while others believe that "Immediate Past President" refers to the results of the previous election and, therefore, Person B has become both the President and the Immediate Past President in the 1999 election. - Joan Malak, Jul. 11, 1999
A:
I'm unaware of any organization that would consider Person B to be the IPP.
In 1999, Person A would remain the IPP.
The reason for the office of IPP is that he or she is a recently experienced officer who can advise the current administration on matters of continuity.
If a presidential re-election "bumped out" the IPP, the Board would lose this value.
Note that the President of an organization that did bump out the IPP at re-election would not carry two votes (those of President and IPP), unless this is explicitly stated in the bylaws.
The same would be true of a person who held, for example, the offices of Secretary and Treasurer.