Why do some items survive time travelling in Majora's Mask?

The Zelda wiki:

When Link plays the song, time is reset, erasing his progress in Termina, and also depriving him of consumable items, such as Rupees and ammo. However, Link will retain the rest of his items, and any Owl Statues which he has awakened will remain active, allowing Link to use them as warp points and temporary save points. Using the items he retains, Link can progress to new areas even after looping time.

Basically, you don't need items you consume to progress through the game. But you do need the items you retain to progress since they aid you in your journey (sure consumables help too, but they aren't as/not necessary).

Unfortunately Nintendo isn't really one to come up with any serious "lore" about any of their series, they just like to create games that people will enjoy. Therefore, any questions along these lines will likely be either speculation, or "because Nintendo made it that way."

So in this example, from the top of my head, a theory might be simply because Link (physically) holds onto certain items, while expendable items are not so important; simply put.

However, tying that into the flow of time within the game, well, there are strange powers at work, and depending on which theory you follow (like the "Link is dead" theory for example), to many, the world of Termina doesn't quite follow the normal rules - either being a construction of Link's mind as some kind of Purgatory, or even some form of jail that Majora is attempting to escape from.

TL;DR: The lore of the LoZ game series is near non-existent, and is really up to the gamers to come up with the explanations for these types of events, as the only hard proof of anything within the series that Nintendo has provided is the timeline itself.

That being said, while they have created a separate Manga Series and Hyrule Historia, this should not be compared with the games, as there is a lot of contradictory material between the two.

They don't ignore just a few sentence, they ignore the intro of FSA (where was say, that the Link is the same from FS), they ignore the Ganonconflict, they ignore just fakes how zelda and link doesn't know each other*

There is evidence that, at the very least, the notion that OoT and ALttP are one and the same cannot be correct. [...] "Link, thanks to you, I was able to escape from the clutches of evil. Thank you!...The Triforce will grant the wishes of whoever touches it, as long as that person lives... That is why it was hidden in the Golden Land. Only a select few were told of its location, but at some point that knowledge was lost... The one who rediscovered the Golden Land was an evil thief named Ganondorf. Luckily, he couldn't figure out how to return to the Light World..."*