> How has the military (US, or other) historically managed to recruit and retain their medical corps, or the Army Corps of Engineers? Has there just not been a situation in modern memory where there weren't doctors sufficient to keep the gears of war turning?

The problem I saw when I was in was that the retention problem was one of incentives. Enlisted folks who work on offensive cyber are sitting next to people who are making far more than they are for nearly the exact same job, minus the aspects of being a soldier (long hours, no OT, tasks outside your core job). Being a contractor just pays more for less, so they have little reason to stay in when the promise of a better life isn't quite what their recruiter told them.