Why are Concepts not Impermanent?

As Buddhists, we should not take seriously those who engage in unsubstantiated speech. Whether or not what the poster said is true according to his beloved Abhidhamma Commentary is irrelevant. The poster has not provided any links to relevant texts, which makes their speech unsubstantiated.

At the DhammaWheel links, in defense of this unsubstantiated speech, another poster of unsubstantiated speech said:

What Eko Care has said is correct according to the Classical texts. The conceptualizing in mind is the impermanent one, but not the Conceptual-object of Conceptualizing-mind. Pannatti is an object. This fake object is perceived by the impermanent mind.

In the Suttas, all conditioned things are impermanent, including objects perceived by the mind. There suttas explicitly on this subject, such as:

If anyone says, ‘mind-objects are self’, that is not tenable.The arising and vanishing of craving is evident...

MN 148

Bhikkhus, Forms are impermanent... Sounds … Odours … Tastes … Tactile objects … Mind Objects are impermanent. What is impermanent is suffering. What is suffering is nonself.

SN 35.4

Ignorance is impermanent, conditioned, dependently arisen, subject to destruction, vanishing, fading away, and cessation.

SN 12.20

To my understanding, only two things are not impermanent.

The first is Nibbana, based on Ud 8.1 and Ud 8.3.

The second is the three marks of existence, based on AN 3.136.

For other concepts - let's take the example of the concept of a chariot from SN 5.10. If no one thought of it, would the concept of a chariot arise and exist on its own? I don't think so.

“There is, mendicants, that dimension where there is no earth, no water, no fire, no wind; no dimension of infinite space, no dimension of infinite consciousness, no dimension of nothingness, no dimension of neither perception nor non-perception; no this world, no other world, no moon or sun. There, mendicants, I say there is no coming or going or remaining or passing away or reappearing. It is not established, does not proceed, and has no support. Just this is the end of suffering.”
Ud 8.1

“There is, mendicants, an unborn, unproduced, unmade, and unconditioned. If there were no unborn, unproduced, unmade, and unconditioned, then you would find no escape here from the born, produced, made, and conditioned. But since there is an unborn, unproduced, unmade, and unconditioned, an escape is found from the born, produced, made, and conditioned.”
Ud 8.3

“Mendicants, whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles: all conditions are impermanent. A Realized One understands this and comprehends it, then he explains, teaches, asserts, establishes, clarifies, analyzes, and reveals it: ‘All conditions are impermanent.’

Whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles: all conditions are suffering. A Realized One understands this and comprehends it, then he explains, teaches, asserts, establishes, clarifies, analyzes, and reveals it: ‘All conditions are suffering.’

Whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles: all things are not-self. A Realized One understands this and comprehends it, then he explains, teaches, asserts, establishes, clarifies, analyzes, and reveals it: ‘All things are not-self.’”
AN 3.136

the way in which the question is formulated is non-sense. concepts are mental constructs, sankhara. and all constructs, material and mental, are impermanent, sabbe sankhara anicca. from a buddhist perspective it is very straight forward and non debatable, actually.