No. It makes no mention of a specific set of clothing nor does it in any way imply that the set of clothing has to remain the same between changes.
Step 1: change armor to a set of clothing.
Step 2: change armor back
Step 3: change armor into a different set of clothing.
Both changes satisfy the condition of being "a set of clothing". If only one appearance could be assumed, the wording would have to be something like "Upon command, the armor changes shape and form to assume the appearance of one normal set of clothing, chosen at the time of the enchantment.
Another example:
I ask you: "Hand, me a pen, please."
You give me your favorite blue pen.
Later I ask you again:
"Give me a pen, please"
Nothing in my wording implies that giving me a different pen would be somehow wrong.
Q 137
What is the DC to disbelieve the glamer on a suit of glamered armor?