Say you have an Amulet of Health +2 and you're level 10, so it's giving you 10 HP. Wild Shape says this:
Any gear worn or carried by the druid melds into the new form and becomes nonfunctional.
However, Alternate Form (which what Wild Shape follows), says this:
The creature gains the physical ability scores (Str, Dex, Con) of its new form. It retains the mental ability scores (Int, Wis, Cha) of its original form. Apply any changed physical ability score modifiers in all appropriate areas with one exception: the creature retains the hit points of its original form despite any change to its Constitution.
Given that, I've got a player making the case that because HP stays fixed when you Wild Shape, it stays as it was when the item was active. That is, he keeps the +10.
It seems to make more sense to me that the Amulet would deactivate and you'd lose the bonus HP from it, and then your HP stays at whatever it would be at that point (since it's not adjusted to the CON of your new form). That is, he loses the +10. In this case, a Wildling Clasp would let the Amulet continue working and thus he'd keep the +10, which is how pretty much every other item works (and I do like consistency).
Any suggestions on which one it is?