Does it break after 2 of the more difficult enemies like everything else? Then who cares!
Zelda is made for the ultimate consumer society, nothing lasts, everything is made to break two steps out the door.

As far as I heard, it does not break. But the attack power degrades over time, you seem to need it for the better ending.
And I really don't know a single place where you need more than two stamina upgrades to get to.

I have 3 stamina upgrades (6 hearts) and there are still places I come up short on being able to climb. My next two are going to be stamina so i have a full second wheel.

I think it was a video but I though I heard there are 190 shrines (47.5 upgrades one way or the other) has anyone else heard this?

That's exactly my ratio as well , people forget just like temporally increased hearts you can increase  max stamina by cooking.

The number of shrines iirc is 120 plus you have the 4 dungeons.

I discovered 2/3 of the map and could climb absolutely everything so far with a little use of strategy. Nearly all towers that seem too high have high hills right next to them, so stamina is not required. And you always find a way to climb the highest mountains with little stamina use. Often you can just run instead of climbing, consuming no stamina at all. Or climb it in smaller portions.

I was really disappointed that the 3rd stamina upgrade is so small and will not upgrade any further and prioritize the hearts required to obtain the master sword for the time being. Also if it rains, and it rains quite often, stamina is useless for climbing but hearts keep their function.

Stamina is also used for charged attacks and slowing down time with the bow.

I'm focused on hearts because I want to grab the Master Sword, and like others, stam has been a non-issue for me with only one upgrade in it. It's just about hunting for the best cliffs to get to those trickier shrines. There's one on top of a tall stone spire in northern Akkala, and if I tried climbing it, failure. Instead I just ran around up a cliff, took a glide across, and climbed the last 15 or so feet to the top. The environment is versatile enough that large amounts of stamina are rarely a necessity.

I think the only exception so far is this giant labyrinth thing off the coast of northern Akkala. I tried gliding to it, but I didn't have enough stam to make the whole journey. I can just cook up some stam restoration food though and solve that problem. Food use swings both ways.

Ah, I'm not worried about the ending for a long time. Plus it's not about being able to climb there, it's the convenience of being able to jump all the way up. Much more fun exploring when you can quickly run up most cliffs and pillars. Together with Gavali's power no more slow climbing anywhere. I have 7 stamina upgrades currently, 3 to go before investing in hearts. Still 9 sections or provinces I have not even been too before focusing on the ending, plus plenty left in 3 others I have unlocked the tower for yet not fully explored.

Since I'm playing without using fast travel, stamina is very useful for efficiently getting around. I use stamina all the time, hearts not really, just don't get hit :)

Ahh, so 40 for stamina, leaves 20 extra hearts + 4 from dungeons, 27 total.