Does the Hylian Shield Break?

While the Hylian Shield has a vast amount of durability, unlike the Master Sword it's not invincible and can break. If that happens, it won't no longer appear inside the Hylian Castle Lockup, and instead must be purchased from a special vendor after the end of a long quest.

Can you get the Hylian Shield after it breaks?

Zelda: Breath of the Wild guide: How to get the Hylian Shield. We found out the hard way that the Hylian shield can break, though it takes a heck of a beating before it does. If that happens, you won't find it again in the castle. Instead, you can buy it from the hidden merchant, Granté, in Tarrey Town.

How many hits does it take to break the Hylian Shield?

The Hylian shield, assuming it has not taken any damage before, can withstand 27 guardian blasts before breaking. It will only break after a single blast if it has taken substantial damage beforehand. This should give you some leeway in case you don't parry.