James Coull, vice chairman of Massport's board of directors, said the decision to quit was Buckingham's alone, and the board had wanted her to continue in the job.
In it, he said he had "been unable to reach a satisfactory agreement" with Ms Coull over a dispute and added it was "unlikely that your wedding will proceed there".
Det Chief Insp John Coull said the soldier, who was based at Brompton Barracks in Dock Road, Gillingham, was in a drunken state in an area close to the river when he was last seen.