Your maximum stamina will gradually decrease over time. You can recharge your stamina by eating Rations, Steaks (Well-Done restores more than Rare)and Energy Drinks. Dash Juice and Mega Dash Juice can also be consumed in order to temporarily give you unlimited stamina. The Hunting Horn Song "Negate Stamina" also temporarily grants unlimited stamina. If you're in a cold climate (your bar will be blue) your maximum stamina will decrease faster, but you can use a Hot Drink to negate that. The Cold Res skill and Hunting Horn song will counter the coldness effect as well (although Cold Res -10 will make the effect worse). Certain Feylne Chief food combinations you can eat before a quest will increase you maximum stamina as well.
There are also skills which will influence your maximum stamina. Ferocity makes it so that "Steaks temporarily grant unlimited Stamina." Carnivore also grants unlimite stamina for eating Steaks, and also you to consume Raw Meat to regain lost stamina. Gluttony +10 makes steaks grant more stamina when consumed, and the +15 version gives all items a chance to grant stamina when consumed. The Eating skill doesn't impact you maximum stamina, but does allow you to eat meat quicker (or slower,if you have the -10 version). The Hunger skill will make halve max stamina depletion at +10, and remove it all together at +15. The -10 and -15 versions will increase the depletion rate.
It's also worth noting that Waterblight and Iceblight are conditions which can be inflicted when being hit by water and ice elemental attacks. They don't impact your maximum stamina consumption/recovery, but they do impact your stamina. Waterblight makes stamina regenerate slower, and Iceblight causes all your stamina consuming actions to use more stamina. Both of these effects will wear off over time, but you can also use a Nullberry to get rid of them. There are also several other skills which impact your stamina consumption/recovery as well, and you can find list of those skills (and all other skills in the game) here.