The spell Mirror Image states the following:

A duplicate's AC equals 10 + your Dexterity modifier.

However - if you were to cast Mirror Image, and then change your DEX (e.g. by equipping/unequipping an item, or being affected by a spell, etc) would the AC of the Mirror Image Duplicate change to maintain $(10+DEX)$, or would it remain at the original AC it was cast with?

(This has been 'promoted' from a musing I made as a comment on the question"Is it possible to increase the AC of a mirror image duplicate?")

A duplicate's AC changes as your Dexterity changes

The spell's description doesn't explicitly say one way or the other whether the AC is calculated at the time of the spell's casting or whether it changes real time, which means we need to apply logic to get to the bottom of this one.

AC is defined in the PHB (pg. 14):

Armor Class

Your Armor Class (AC) represents how well your character avoids being wounded in battle.

Furthermore, the mirror image spell description says (PHB, pg. 260):

... the duplicates move with you and mimic your actions, shifting position so it's impossible to track which image is real.

These two statements and the fact that the duplicates' AC is derived from your Dexterity implies that the duplicates must be as dexterous as you are, and that they only "dodge" an attack because you were capable of doing so (i.e. if the attack was aimed at the "real" you, you would have been able to dodge it).

If your Dexterity changes during the duration of the spell, then you are more/less dexterous now than when you cast the spell, and thus better/worse at dodging attacks. Given that the duplicates "move with you and mimic your actions", it stands to reason that they must now be as dexterous as you have become, since they must still be capable of dodging what you can (or can't) now dodge.