The old Disrupted/Demoralized bit (again)

[joe_oppenheimer]

Not sure where the half morale thing comes from. That would make recovery almost impossible.

Demoralized units have their morale reduced by one as ployd says above.

One subtle thing about morale in the game is that when you take a morale check in combat you need to roll equal to or less than your morale, but for recovery you must roll less than your current morale.