Is the Hylian Shield subject to the same durability that other shields in the game are or is the shield indestructible?
Unfortunately, the answer is yes. The Hylian Shield can be broken and will wear down, just like every other shield in Breath of the Wild. It is unfortunate that this shield does break, but it is what it is. Best to save it for when you want to take some nice screenshots. There are plenty of other shields in the game with better defense anyway.