Does magic item hardness remain in an anti-magic zone?

[Feldar]

Making an item magical increases its hardness, but is that a permanent change to the item or is it tied to the continued operation of the magical aura? If a magical item is inside an anti-magic field, does the extra hardness remain?

[Biggus]

The nearest I can find to an answer is in the Rules Compendium (p.11):

A magic weapon used to attack from inside an antimagic area, or one used to attack a creature inside an antimagic area, gains none of the benefits of its magic properties.

This doesn't technically answer your question RAW, as it specifies "used to attack" and hardness is a defensive property, but the "gains none of the benefits" part definitely implies that it would lose its extra hardness and HPs.

[Feldar]

If the hardness increase is a benefit of the process of enchanting an item, that's definitely on point.

The hardening spell (SpC p 109) is a permanent Transmutation spell. Would the effects be reversed in an anti-magic field? If so, would they return once the anti-magic field ceased to exist?

Wall of stone creates a permanent wall of stone. Would it cease to exist in an anti-magic field? If yes, would it re-appear once the anti-magic field was no longer?

If folks have anything on point about this I would really appreciate it, as it's about to become an issue in an ongoing campaign.

[Biggus]

If the hardness increase is a benefit of the process of enchanting an item, that's definitely on point.

The hardening spell (SpC p 109) is a permanent Transmutation spell. Would the effects be reversed in an anti-magic field? If so, would they return once the anti-magic field ceased to exist?

It would be reversed in an AMF:

A spell’s Duration entry tells you how long the magical energy of the spell lasts.

Permanent
The energy remains as long as the effect does. This means the spell is vulnerable to dispel magic.

While this quote doesn't specifically mention AMF, it does make clear that a permanent spell only works as long as the magical energy is in effect, so it would be affected by AMF.

Also, antimagic is "stronger" in terms of what it can affect than dispel (for example, supernatural abilities are affected by AMF but not by Dispel Magic) so if it can be dispelled, it should also be vulnerable to antimagic.

It would return afterwards though:

An antimagic field suppresses any spell or magical effect used within, brought into, or cast into the area, but does not dispel it

Wall of stone creates a permanent wall of stone. Would it cease to exist in an anti-magic field? If yes, would it re-appear once the anti-magic field was no longer?

Wall of Stone is different, its duration is instantaneous, not permanent:

Instantaneous
The spell energy comes and goes the instant the spell is cast, though the consequences might be long-lasting.

Once created, the wall of stone is non-magical, so it's unaffected if an AMF covers it later.