All originalists acknowledge the “dead hand” problem, and so all agree that the normative case for originalism depends on the amendment procedure being adequate for keeping the constitution up to date. Or at least all of the originalists I have talked to (n=1). Yet it can be shown that the Article V amendment procedure is unlikely to be adequate, and the probability that it is adequate across time is virtually nil.
The reason is that outcomes produced by voting rules depend on the number of voters (and also the diversity of their interests but I will ignore that complication since it only reinforces the argument). An easy way of seeing this is to consider the strongest voting rule—unanimity—and imagine that people flip a coin when they vote (the coin flip reflects the diversity of their interests, not a failure to vote their interests), and can agree to change a law only when all voters produce heads. The probability of achieving unanimity with a population of 2 is 1/4 (only one chance of two heads out of four possible combinations), with a population of 3 is 1/8, and so on.
For a more rigorous formulation, consider a spatial model from 0 to 1, with a 2/3 supermajority rule. The status quo is chosen randomly (on average 1/2), and the population chooses whether to change it. If the population is 3, voters will change the outcome with probability of (near) 1, because 2 of the 3 people will draw an outcome greater than or less than 1/2 with probability of (near) 1. If the population is 6, there is now a non-trivial probability that 3 of the 6 people will be on one side of 1/2, and 3 people on the other side, so a 2/3 majority (4 people) will be unable to change the status quo.
The U.S. population has increased from 4 million at the time of the founding to 300 million today. If the amendment rules were optimal in 1789, they are not optimal today. If they are optimal today, then they won’t be optimal in a few years. Originalism with a fixed amendment process can be valid only with a static population.
There is a related argument that one can make based on the Buchanan/Tullock analysis of optimal voting rules. Thanks to Richard for a helpful email exchange.