Are you using box traps (a.k.a. live traps), snap traps, or glue traps? Is the issue that the mice are being eaten, or that something is taking your traps away?
Many creatures could eat mice caught in a snap trap, from cats to raccoons to shrews to other mice.
Minimize the time between setting a trap and checking it; this will reduce the time that a mouse is in a trap. Remember to reduce or eliminate mouse harborage in order to decrease an area's attractiveness to rodents.
Consult other FAQs on mouse control.
