Disclaimer: everything listed here is based on the cracked, analyzed and reverse-engineered game code, so there was no trial-and-error involved. All credit for this goes to leoetlino AKA Léo Lam, and their way more in-depth and well-sourced guide can be found here: https://zeldamods.org/wiki/Object_respawning
Breath of the Wild has a ton of different materials, weapons, enemies, etc. and most of them respawn. A couple of them are sadly still permanently missable but compared to other games of that scale, it's mostly foolproof.
A common misconception is that the Blood Moon resets everything - but you can easily disprove that by just breaking an ore deposit or cutting down a tree before the cutscene hits - it will not have respawned afterwards. The ONLY things the Blood Moon resets are weapons / bows / shields in the overworld and non-boss monsters. Everything else either respawns by one of a myriad of wildly different other conditions, or not at all.
Just an example:
There is an Eightfold Blade in a rock on a hill near Kakariko. If you take the sword and toss the rock away, both are gone. If you now get a Blood Moon without leaving the area, the blade will respawn, but the rock won't, resulting in a floating sword.
Also, for many of the mechanics, it is important whether or not Link is on the same map unit as the item. Those map units are mega large, each one about the size of the Great Plateau, so when the code calls for Link being on a different map unit than the item, you have to be far, FAR away - not just out of sight or out of spawning distance.
Now for the actual respawn mechanics:
Shop items:
Items sold by merchants, wandering traders, Beedle etc. respawn every in-game midnight, but only the ones that are on a different map grid as Link: e.g. if you spend the night in the Lost Woods (F-2 on the map above) all shops in Hyrule restock EXCEPT the ones inside the Deku Tree. You can just skip time at a fire/inn and it will still count.
Exceptions:
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Shops that never "use up" items, like the Akkala Tech Lab, do not need to restock.
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Granté's Hylian Shield replacement only restocks if you owned the original Hylian Shield before AND broke/lost it.
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Arrows only restock if the player currently owns less than 50 of a certain kind
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Also, the game treats the 16 Beedles on the map as separate, individual merchants, so if you made Woodland Stable Beedle restock, then Kara Kara Bazaar Beedle might still not have new items.
Blood Moons (RevivalBloodyMoon)
See here:
(I had to make room because Lemmy.World posts aren't allowed to be more than 10k characters long)
No automatic revival (RevivalNone)
This is exactly what it sounds like: actors that just flat-out never respawn, like Master Kohga and the Blights. Some "one time use" items are the metal cubes for Korok Puzzles or shrine puzzle orbs, which vanish once you complete the puzzle.
Less obvious is that this also applies to treasure chests, regardless of whether or not the item INSIDE would otherwise respawn. The Hylian Shield for example is actually prorammed to respawn and would do so if it was lying around in the overworld. But the chest never respawns, so the shield won't either.
Once you won one of Selmie's Shields from the respective shield surf course, it vanishes from the wall inside her hut permanently. The next time you win, you'll get rupees instead of a new shield.
Exceptions:
- Chests only count as "looted" if you actually took the item(s). If you open a chest with a full inventory, Link will close it again and the chest will not despawn.
No drop revival (RevivalNoneForDrop)
This is basically the "RevivalNone" mechanic, but it only applies to items inside of certain "containers". For example, you can loot every broken Guardian only once, and the ones that can be flipped over also generate their extra loot only once. Broken wagons usually have 2 treasure spots, so you can loot each "end" of the wagon once.
No revival for use (RevivalNoneForUsed)
Again it's the "RevivalNone" mechanic, but for actors without loot. For example, you can activate every Sheikah Tower only once - the terminals will never revert to their un-activated state. Likewise you can only complete each Korok Puzzle only once, and use every key inside of shrines only once.
Random revival (RevivalRandom)
This applies to the vast majority of items, and contrary to popular belief, this is completely unrelated to the Blood Moon. Fruit, mushrooms, herbs, flowers, critters and insects with fixed spawn locations, most regular animals like fish, crabs, snails and and some "breakable containers" like ore deposits belong into this category.
These items have a 1% chance to respawn for every minute of active playtime, but only the ones that are not on the same map unit as Link.
The most common situation where this can screw you over are the "Three Trees" Korok puzzles. If you have picked the wrong fruit or the environment messed up the puzzle, it depends entirely on this "playtime and RNG" combo how long it will take for the puzzle to fix itself.
Exceptions:
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Fairies only appear if you have less than 3 in your inventory
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Likewise, Electric Darners and Thunderwing Butterflies only appear during thunderstorms. Tireless Frogs need at least heavy rainfall, and Sunset Fireflies only appear at night.
Random drop revival (RevivalRandomForDrop)
This is the same as "RandomRevival", but applies only to items inside of specific containers, like pots, barrels and crates. The containers respawn every time the zone is reloaded, but if you crack a recently looted barrel again "too early", it will be empty until the loot inside has respawned.
The Lord of the Mountain (RevivalUnderGodTime)
Whenever the Lord of the Mountain appears, the top of Satori Mountain will glow green/blue. During that time, a lot of rare critters are present on the mountain (like a tree full of beetles). These vanish along with the LotM after a while, so you have to be quick to gather them.
At the same time, ALL Blupees on the map respawn, but those stay spawned until Link startles or hits them.
Not listed:
Everything not listed doesn't have special respawn conditions and will reappear every time the zone is reloaded. Barrels and crates, trees, rocks and boulders and certain animals like Cuccos, Sand Seals and horses just constantly respawn. This can be used to your advantage:
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If you're farming wood for Tarrey Town, bomb the log piles near Rito Stable, collect the wood, save & reload, repeat. The logs always respawn and will geenrate a few bundles of wood each time.
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If you want a horse with a specific coat color, save near a wild herd and reload until the desired horse shows up. The Royal White Stallion and Giant Horse won't won't spawn again while you already own them.
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Rock ring / boulder golf Korok Puzzles. If you save & reload, all rocks/boulders are back at their starting positions. The same applies to (unused!) metal cubes and shrine puzzle orbs, so mistakes are easy to fix.
DEspawning items:
Items you dropped will vanish if you walk away, fast travel or reload. The same goes for enemy loot & equipment you don't pick up and meat dropped by animals. Items with fixed spawn locations (like mushrooms, herbs etc.) will not vanish if left alone, but if you cut / hit them so they turn into "loose" items, they will vanish once you go away.
This also happens if there are too many loose items at once (ca. 10). If you drop 15 swords on the ground, you'll only be able to pick up the 10 most recently dropped ones as the first 5 will have vanished.
The only exceptions are items on the weapon/bow/shield mounts inside your hourse - those will NOT vanish on their own. Items dropped on the ground inside your house will still go poof, so you can only store 9 items total.
Source: