From Xanathar’s Guide to Everything:
Walloping Ammunition: This ammunition packs a wallop. A creature hit by the ammunition must succeed on a DC 10 Strength saving throw or be knocked prone.
Unbreakable Arrow: This arrow can’t be broken, except when it is within an antimagic field.
From Basic Rules:
+1 Ammunition: You have a +1 bonus to attack and damage rolls made with this piece of magic ammunition. Once it hits a target, the ammunition is no longer magical.
Because +1 Ammunition stipulates that the magical effect wears off after use but these other magical ammunitions do not, I assume this means their magic is persistent. Further, the DMG states that magic items are as durable, if not more so, than common items. However, the PHB also states (without any exception that I could find for magical ammunition, emphasis added):
Ammunition. You can use a weapon that has the ammunition property to make a ranged attack only if you have ammunition to fire from the weapon. Each time you attack with the weapon, you expend one piece of ammunition. Drawing the ammunition from a quiver, case, or other container is part of the attack. At the end of the battle, you can recover half your expended ammunition by taking a minute to search the battlefield.“
How does this resolve according to strict interpretation of RAW? Does Walloping Ammunition have a 50% chance of disappearing after use? Does RAW prevent a PC from spending more time searching for the arrow? Is there special consideration for magic items that I’m missing?
Ammunition is ammunition by Rules as Written (RAW)
TL;DR According to the RAW, half of the ammo you fire, magical or not, is not recoverable regardless of how much time is spend searching.
Recovery Mechanic
Lacking a More Specific Rule, Half is Recoverable
Half of the ammunition you expend is recoverable as cited in the rule. Lacking a more specific mechanic for recovering ammunition, that is the case for both magical and non-magical ammunition. Walloping ammunition does not have a more specific recovery mechanic.
Time Spent Recovering Ammunition
By the rules, if the character spends a minute searching, they recover half the spent ammunition. There is no provision in RAW for spending more time searching to recover more than half.
Recovery Narration
The mechanics of recovery do not specify why ammunition is unrecoverable. It may be broken, lost, or lose it’s “umph”. The narration of the mechanic is up to the DM.