When you put Moga to nap in your home base they completely recover their HP and Ability points. The amount of time that the Mogas spend napping is dependent on the their level.

Level 4: 10 Minutes
Level 5: 15 Minutes
Level 6: 20 Minutes
Level 7: 25 Minutes
Level 8: 30 Minutes
Level 9: 40 Minutes
Level 10: 50 Minutes
Level 11: 60 Minutes