The combat system in Legend of Zelda: Breath of the Wild is made all the more varied - or frustrating, depending on your point of view - by the fact that all of the weapons and shields in the game have a durability stat, meaning that they'll shatter into a million bright blue pieces once you've clobbered enough enemies, or deflected enough blows.
If you're pining for something that isn't quite as fragile, you're in luck. There are a few weapons and one shield in the game that are almost unbreakable.
The Master Sword is the only truly unbreakable weapon in the game, but there are a few other items that can either be reforged, or that have a very high durability stat.
This is as close as you're going to get to weapons that don't break, so make your peace with that and go get 'em.