Why my max health is capped at 50% of the bar in Dark Souls 2?

Solution 1:

When you first start a new game, you start out "hollowed" with your health capped at 50%. To regain your human form and 100% health cap, simply walk past the first intro area and you will regain your humanity after the character creation.

After that, every time you die (or get cursed), you will gradually lose some of your maximum health down to a minimum of 50%. You can regain it by using¹ a Human Effigy, a consumable item found in limited supply around the world, or by using a White Sign Soapstone and helping another player successfully defeat a boss.

There is another way to regain your humanity which does not depend on limited items or online play, but it doesn't become available until near the end of the game.

After the Demon of Song boss fight in the Shrine of Amana, there is a door which only opens when you are in hollow form. Inside this door, past a handful of enemies, there is a fire. If you pray at this fire with no Human Effigies in your inventory, your humanity will be restored. There is also a convenient bonfire just before this door so that you can easily travel here when you're out of effigies and need to regain your humanity.

There is also an item which reduces the health penalties from dying.

There is a ring called the Ring of Binding which can be found just outside the Cathedral of Blue near Heide's Tower of Flame, which reduces the health penalty and increases the minimum health cap from 50% to about 75%.

_{¹ You need to use the Human Effigy from the inventory screen or by equipping it in your item belt. Do not burn it. If you burn it, it instead reduces the likelihood of invasions and blocks you from summoning phantoms.}

Solution 2:

According to this article dying removes health from you permanently. That means if you die too often you only have Half HP, losing 10% for each consecutive death. You can return your health to its normal value by using a Human Effigy from your inventory. Also, Curse can inflict the same status, to the same degree with each infliction, and is cured in the same way.