Fighters will regain stamina when in an inactive state. This means you recover the most stamina when standing still or when you have distance between yourself and your opponent.
Why Do I Lose Stamina so Fast?
1. You need to be more thoughtful about how much you attack and how.
2. High-risk moves that whiff wreck your stamina. Only use them when you are pretty certain they will land.
3. Non-combo list strikes will waste stamina even when they do hit.
4. On a related note to 3. Use the combos your fighter has, and you will burn less stamina.
5. Damage recovery is slightly slower than stamina loss from strikes. You can start a combo rock someone back off, and then come back in and do another combo to knock them out. If you were to rush in, you would likely lose stamina trying to force the knockout.