Stamina System - Has this been done?

I had an idea for a stamina system that I think is elegant and evocative:

• Each player has a stamina score, somewhere around 7-12
• Each player gets one action each turn
• You can choose to gain an extra action on your turn. If you do, roll 2d6. If you roll less than your stamina, you take the extra action and can even repeat this process to take another extra action. If you roll equal to or higher than your stamina, your stamina decreases by 1 and you can't take any extra actions after this one.
• Each action carries some cumulative penalty that is added to your stamina roll. This penalty resets each turn.

Is there any system that uses stamina in this way? Are there any glaring pitfalls in this concept? I think it would be really fun to push your luck to potentially get to take many actions in a turn, but risk tiring yourself out.

Some other thoughts

• Getting hit by attacks should deplete stamina
• Dropping to stamina should be defeat