Stamina recover time is based on the fleet's privacy settings. The fleet captain can tap the fleet menu at the upper right of the Epics page to adjust these settings.
Public Fleet: This happens if a captain has not picked the "invitation only" option when he/she creates the fleet. A public fleet will show up on the public list of fleets so that anyone can join! Its stamina recover time is 10 mins.
Invite-only Fleet: This happens if a captain has picked the "invitation only" option when he/she creates the fleet. Only invited players can see the fleet's details. Its stamina recover time is 1 min.
If the fleet captain has already launched the fleet, the fleet settings can no longer be adjusted. Note that a fleet will automatically launch 6 hours after its maximum member capacity has been reached.
*Reaching maximum member capacity means: if, for example, your fleet has been set to allow a maximum of 8 members, then 8 members must join the fleet for it to be considered at full capacity.
After this happens, a 6 hour countdown will begin. However, if any members leave the fleet during these six hours, you will need to wait for the fleet to again reach maximum member capacity for the 6 hour countdown to begin again.