JFK reappointed Dulles to head the CIA in 1961. It was after the disastrous Bay of Pigs invasion of Cuba that Dulles resigned.
Maybe it was a "forced resignation", designed to take the heat of of President Kennedy for stupid decisions.
If Dulles lusted for power, as some have alleged, then it would make sense.
Allen Dulles absolutely lusted for power. Read "The Devil's Chessboard." It makes sense.