Muscovy females suddenly disappearing

[Miss Lydia]

Maybe something spooked her and she flew off. Once in the air everything on the ground looks the same to them if there are houses around, Have you checked every yard in your neighborhood?
when she has been broody where did she make her nest?

 

[MartinFamilyHomestead]

Do you lock up your ducks at night? Something could be getting after them. Some predators will take whole birds and leave no trace. However Muscovys go broody very easily so they could be laying on nests, I would expand your search past your own property. I would be very concerned with then being out and about for long period of time exposed to any other animals.