Was the Constitution of the United States meant to be perpetual?
Yes, the Constitution of the United States was meant to be perpetual, subject to the amendment procedure contained in the Constitution itself.
There are two possibilities, either it was perpetual, or it was intended to cease to be effective at some point in time that is defined somewhere.
No court or legal scholar has ever seriously suggested that the Constitution had an expiration date. Neither does any legislation ever adopted (apart from the efforts of the former Confederate States to leave the Union without its consent which was repudiated by the U.S. Civil War and related legal and political proceedings).
As Nate Eldredge noted in a comment, the preamble of the United States Constitution states that it was adopted "secure the Blessings of Liberty to ourselves and our Posterity".
The fact that the Constitution contained a transition provision in relation to its "natural born citizen" requirement for a country that didn't exist prior to 1776 does nothing to change any of this analysis.
The founding fathers had no authority to bind anybody but themselves.
The assumed rule that someone has no authority to bind anyone but themselves is not now, and never has been, the law.
The authority of people to bind people other than themselves, including successors who aren't even born yet, to legal documents, is long standing in both Western and Eastern legal systems.
Agents can bind principals. Employees can bind employers. Union officials can bind their members. Partners can unilaterally bind each other. People creating trusts can bind the trustees and beneficiaries of the trust long after they are dead; charitable trusts can be perpetual. Military officers can bind their subordinates. Parents can bind their children in many jurisdictions. Guardians and conservators can bind their wards. Executors of estates can bind a decedent's heir and devisees. Home owners associations can bind member property owners and their guests. Governments can bind their residents. Sovereigns can bind their subjects.
Before the modern concept of property arose in the early modern period (i.e. prior to around 1500 CE), real estate ownership was primarily hereditary and inalienable, as was the serf-lord relationship. Transfers of property are not undone when the person who makes them ceases to exist. Real estate covenants routinely "run with the land" after they are created by the current owners.
The legal obligations you enter into while you are alive are binding upon your estate at death. In the civil law countries with legal systems based upon those of Continental Europe (derived in turn from Roman law), the default rule is still that the obligations of a decedent are binding upon the decedent's next of kin, although it is not terribly difficult to opt out of that default rule in the heir's discretion after death if they elect to do so (and many do). Until not long before the Industrial Revolution, in the late early modern period of history, most Western legal systems, and East Asian legal systems, provided that your descendants continued to be bound by your debts and could not opt out of that obligation.
When a legal entity is bound, all successor owners, directors, officers, managers, and partners of the entity are bound perpetually by anything done by someone with apparent authority to do so and by judgments entered against the entity.
The United States of America is, of course, a legal entity which is not operated for profit, so the ability of its founders to bind successive generations is a pedestrian principle that follows from ordinary non-constitutional law anyway.
A treaty between nations are binding long after every single person who signed of on it is dead.
The assumed rule that someone can bind only themselves simply does not pass even casual examination.