Bullhockey.
Saying that an ineligible office holder voids the Constitution is like saying that a murderer who "gets away with it" voids the statute against murder.
It is the violator/usurper who needs to be replaced, along with all who abetted him, not the legal document they violated.
Federalist/Anti-Federalist and Constitution ping. This article is about a month old, and it appears I missed it.
A basic tenet of a constitutional republic is that all law is authenicated, published and archived. The federal courts are authorized to accept copies of the originals if a reasonable assurance can be made the originals are archived and maintained by a President and his officers who are not in violation of the US Constitution. Evidence must be preserved and protected by individuals authorized by the Constitution or the evidence is tainted.
The President is the Chief Executive Officer of the US federal government. An ineligible President voids the Constitution and all US law, rules, regulations, treaties and executive orders because the chain of custody of preserving and protecting the evidence of US law is destroyed.
There are many reasons the Constitution requires an eligiible President at all times. One of those reasons is to maintain the chain of custody of US law as evidence of law in the archives. Only an eligible President can appoint or delegate authority to the Archivist of the United States.