To the people who still need confirmation: yes, the star does reappear after a while. I think it was around three weeks for both time capsules I buried. They won't ask you to bring it back; once you dig it up you just need to bring it to them and they'll show you the letter and present with it.
Also, I know the place I digged them up was a few spaces away from where I'd buried them because I planted flowers on the original spot. So they don't disappear, they just move to the closest open space. I assume it works the same for patterns.