If we could get back to Chuck Hagel, the Secretary of Defense on the way out ... and for that matter, who was Abe Lincoln's secretary of war?
He had two.
Simon Cameron Pennsylvania
March 5, 1861 January 14, 1862
The gent obviously was unable to cope with generals and with the war in progress in 1862.
Edwin M. Stanton Pennsylvania
January 20, 1862 May 28, 1868
Outlasted the president and served president Andrew Johnson as well.
However, he was one of those radical reconstructionist
's who eventually pissed off President Johnson so badly that he was fired. Johnson, like Lincoln, was not in favor of the Radical Reconstruction. His intent was to heal the nation's wounds. The RR's were all about rubbing salt into the wounds.
Stanton being fired led to the impeachment of President Johnson. For all that Stanton was a right prick, he handled the cabinet post well enough.
Secretary of War or Secretary of Defense: the cabinet position is one where one serves at the pleasure of the President. If the President isn't pleased, you get sacked.
Best wishes, Chuck Hagel, and thanks for the effort.