I searched expecting to find a military wavier. Instead I found that no member of the U.S. Army in Alaska may carry a concealed weapon on or off base by order of Major General Charles H. Jacoby Jr.
http://www.usarak.army.mil/policies/PUBS-ACROBAT/USARAK_Policies/CGCOFS%20POLICY%20STATEMENT%2020.pdf
Don't we have Navy & Air Force bases there also? His order would not be in effect on them. Also, what about those that are discharged (medically or otherwise) and are still under the age of 21, they are still being barred by the state and his order would also not effect them.
While within his power, its pretty stupid to treat your soldiers as less responsible than the local civilians of the same age group.
I don't know about the Army, but the Air Force at least allows carry of shotguns and other anti-bear weapons on it's Alaskan bases.