Do the hidden items in the mirage spots respawn?

Question

If I pick up a hidden item, when the mirage spot comes around again another day, will there be another hidden item (either the same item or a different one)? I've seen this on Serebii:

'With the items, the hidden items only appear one a day and at random between a selection of three. These also will only appear in the area that's indigenous to your game for the day, and not through any found via StreetPass or PassingBy. The Dowsing Machine items available are based on the island type and are as follows'.

This appears to imply that they do, so I need clarity as I have no evidence either way.

Answer 1

Not Necessarily.

Mirage Spot items are no different than regular items that you find located on the map. It's sort of a one-obtainable thing. Although, some hidden items appear, but not all - like the "Honey" in X/Y. There's a chance, but not as likely - more likely since their hidden. So, your chances are unpredictable

Comments

some one answered before but I posted a comment with new information and he hid his answer with it. I've reposted this in the question

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Because my answer was wrong and editing it would be completely changing the answer