Thought this was a Morshu thread. :facepalm:
To answer your question, I think that the items that don't go back in time are part of Link's existence.
Confused? Allow me to explain. Ever notice how you don't see other Links throughout the game, even if you were there at the same place at the same time?
I believe that Link can only exist in one time period at a time. In simpler words, he exists as a singular being in only one 3 day period. Thus, there aren't multiple Links.
If the items are attached to Link's existence, it can only be said that they are singular too, and you cannot find them in a time period other than Link's.
Sorry, I can't make sense of how that works, personally, I believe the are not multiple Links as because most people have said, when you use the Ocarina to return to the first day, you rewinding time. By rewinding time and not time travelling back to the first day, there can be no Link's to exist other than the Link we play as.
You'll notice that for some of the side quests, that if you returned back to the first day before going to attempt them, that you need to go beat some of the bosses again, which although can be a pain for some people and fun for others, explains your question about when Link goes back to the first day, shouldn't he have to beat them again? Well no, it would take too long to complete the game. Most likely the fans would be outraged about how hard the game is to, considering you'd have to beat several temples in 3 days, that even with the Bunny Hood and Reveresed Song of Time, would be impossible. Therefore to make the game more playable, Nintendo put the portals that send Link straight to the boss, explaining your question about having to beat them again, you do. The question about keeping the items you gain in each temple are explained by the fact that Link only rewinds time, he sends himself with all of his items back to the first day (and the fact it stops you having to play through the temples again), although I don't understand why you lose such items as money and arrows.