The description of the spell does not explicitly say in one way or another if the CA is calculated at the time of casting the spell or if it changes in real time, which means that we must apply logic to reach the end of it.
AC is defined in the PHB (page 14):
your Armor class (AC) represents how well your character avoids being wounded in battle.
In addition, the mirror image The description of the spell says (PHB, page 260):
… duplicates move with you and mimic your actions, changing positions so it is impossible to trace which image is real.
These two statements and the fact that the CA of the duplicates is derived from your Dexterity implies that the duplicates must be as skilled as you are, and that they only "dodge" an attack because you were able to do so (ie, if the attack was directed to your "real", you could have dodged it).
If your Skill changes during the duration of the spell, then you are more / less skilled now than when you cast the spell, and therefore, better / worse in the dodging attacks. Since duplicates "move with you and mimic your actions," it is logical to think that they should now be as skilled as you have become, since they must still be able to dodge what you can (or can not) avoid.