In the real world, there are literally two types of stamina in a person's body, each operating with a slightly different body mechanic. One is short term for bursts of speed and power (running or heavy lifting), the other is long term endurance. Both draw from long-term endurance, but non-strenuous activities (such as walking) do not draw from the short-term stamina.
I'll explain in a simple way. Fill a pitcher with water and leave a small opening to pour from. This is your long-term endurance. Now take a small cup and fill it with water from the pitcher. This is your short-term stamina. Sprinting will drain the cup very fast. As soon as it is empty, you can run no more. You have to wait until you refill the cup with some water from the pitcher. If you can fill the cup as fast at you are using it, you can run or jog very far at a slow pace. Endurance training will give you a larger volume in the cup and the ability to fill it faster from the pitcher.
Walking is like taking sips from your short-term stamina (the cup), or directly from the pitcher. Your cup remains full all the time, or refills as you are walking (if you are in shape) if you just emptied it by running. However, you are still draining your long-term endurance, and your large reserve will eventually run dry. This could take hours or days, depending on your condition and surroundings.
So, weak characters should slowly lose stamina even if walking, while strong characters should not lose at all, and in fact rapidly gain stamina while walking, or even jogging.
PlaneShift does not factor in the 'pitcher' in the equation, so you should be able to walk forever once you get to a certain level of endurance. If you lose stamina walking at higher levels, it is a balance issue is all.
I do have a -little- issue with having low stamina to start. 'Peasants' are not the weakest of people in the time period PS is set in, and could work hard all day long with little rest. You start the game as a peasant.
