I think that the last time was sometime in the 50s, after WWII and Korea. I think they finally had accumulated enough incidents of bored, pissed off, stupid, and criminal servicemen who initiated shootings. In WWII infantrymen generally carried their rifles from training to the next training base and then embarkation. They didn’t carry ammo and generally didn’t have the time, ammunition, or the money to get into too much trouble and they didn’t get to carry the rifle on the few liberties they were allowed. During the 50s they stopped doing that, I’m not sure when.
Boredom and stupidity along with a loaded weapon can be problematic. Just last year there was a Russian roulette death in the apartment of some security police airman. In about 1972 two of the gate guards I knew at my Marine Corps installation were bored in the middle of the night and were playing quick draw. At some point, they drew and there was a loud noise. One looked at his pistol and asked what that noise was and the other was holding his side yelling you shot me you sonofabitch. Both were subject to some inconvenient consequences. I witnessed other incidents of people who were drunk, some sober, who were pissed about something or at someone who tried to retrieve their personal weapons from the armory. The one who did manage to get a weapon had to be jumped and disarmed and it was fortunate nobody but him got hurt (severe beatdown).
I spent a career in the military and if they allowed open carry of personal and duty weapons outside of duty there would be more of these incidents.