You don't envision a possible scenario where Hays, Mullins, and Santander are getting an equal amount of rest?
I would think you could play Cowser or Hays in center twice a week with Mullins sitting. If Santander sits once a week and DH's 1-2 times a week, you can still have a split where every outfielder plays 4-6 times a week.
This would make the most sense to me unless the FO is just completely down on Hays. Looking at a larger sample size over the last few seasons, Hays, Mullins, and Santander have been relatively equal players. Hays is not the only outfielder capable of going through extended cold spells. Mullins tends to fall into the same kind of slumps.