[johniegrad]

In 1987 he became the first Naval Academy graduate in history to serve in the military and later be appointed Secretary of the Navy. He resigned as Naval Secretary in 1988 after refusing to agree to a reduction of the Navy's force structure during congressionally-mandated budget cutting.

From his website.

[Seattle Conservative]

I could be wrong about what Mark said, but that's what I remember. Here's what factcheck.org says (all I've been able to find so far except Jim's web site and wikipedia). Sounds like he and Carlucci weren't too happy w each other so maybe it was a 'mutual decision' that he leave:

Multiply by Four
The announcer tells us that Webb "served in the Reagan administration. After 10 months, he quit." This misstates Webb's service. He actually joined the administration in 1984, when he was nominated and confirmed as Assistant Secretary of Defense for Reserve Affairs. The Vietnam veteran, who was awarded the Navy Cross, the Silver Star, two Bronze Stars and two Purple Hearts for his military service, resigned to write another book in 1987, but almost immediately then-Defense Secretary Caspar Weinberger asked him to become Secretary of the Navy.

Webb was confirmed to that post, but it was a short stay. He had conflicts with Weinberger's successor, Frank Carlucci, and didn't agree with the way Carlucci wanted to implement cuts in the Pentagon's budget that had been mandated by Congressional and White House agreement. Specifically, Webb publicly objected to cutting the Navy fleet as Carlucci proposed. Webb's leavetaking was indeed turbulent.
http://www.factcheck.org/article441.html

From wikipedia - Carlucci:

During the early 1970s he became a protégé and was a former roommate at Princeton with Donald Rumsfeld. He was undersecretary of Health, Education and Welfare when Caspar Weinberger was secretary during the Nixon administration. Carlucci became Ambassador to Portugal, and served in this position from 1974 until 1977. Carlucci was deputy defense secretary from 1981 until 1986, national security advisor from 1986 until 1987, and defense secretary in 1987, following the resignation of Weinberger, his nomination by President Ronald Reagan and his confirmation in the Senate by a vote of 91 to 1. He was reportedly less hard-line in policies toward the Soviet Union than Weinberger.

CIA Deputy Director
1978–1981
Preceded by: Enno Henry Knoche
Succeeded by: Bobby Ray Inman

United States National Security Advisor
1986–1987
Preceded by: John Poindexter
Succeeded by: Colin Powell

United States Secretary of Defense
1987–1989
Preceded by:Caspar W. Weinberger
Succeeded by: Dick Cheney
http://en.wikipedia.org/wiki/Frank_Carlucci