David Hardy at Of Arms and the Law has discovered that those restrictions may be coming to an end. He provides a link to a pdf of the entire bill.
This is aimed at base commanders who have ordered that soldiers report and register privately-owned firearms kept at their residences off-based.
The Public Law version is not yet online, but here's a link to the 2011 National Defense Authorization Act as introduced, which became Pub. L. 111-383. Section 1062 (on PDF pages 253-54) provides:
"SEC. 1062. PROHIBITION ON INFRINGING ON THE INDIVIDUAL RIGHT TO LAWFULLY ACQUIRE, POSSESS, OWN, CARRY, AND OTHERWISE USE PRIVATELY OWNED FIREARMS, AMMUNITION, AND OTHER WEAPONS.(a) In General- Except as provided in subsection (c), the Secretary of Defense shall not prohibit, issue any requirement relating to, or collect or record any information relating to the otherwise lawful acquisition, possession, ownership, carrying, or other use of a privately owned firearm, privately owned ammunition, or another privately owned weapon by a member of the Armed Forces or civilian employee of the Department of Defense on property that is not--
(1) a military installation; or
(2) any other property that is owned or operated by the Department of Defense.