How do you refill the beast stamina?

there is no refill. each beast has a set amount of stamina needed, and you only have space for a certain amount of stamina. Hermes takes 5 Stamina normally, so if you make him work you will have 5 less stamina available from you total to let other beasts work.You can increase the total amont of stamina by upgrading the beast workshop or research, but it doesnt decrease over time. The set amount of stamina does not affect beast you can take into fights, only the ones you can put to work.