There are many ways to answer the maintainability question - having documentation available, work with other Perl developers to back each other up on the maintenance issue, take your CMS open source, etc. Its really not that difficult to address.
However, I would guess that the real issue is not maintainability. The clients are more likely just using it as an excuse because they really just want PHP or WordPress or Joomla or something else, because of the status or coolness that they perceive would come with it. Much like the general public, businesses often act like sheep and just want to follow the trends. Or maybe they want to hire the CEO's nephew, but have to jump through the appropriate hoops first. Either way, they'll ever admit it, and you'll have to read between the lines.
Since you have already developed your own CMS, does it really make sense to scrap your investment to start over and develop it again in another language? Is it worthwhile to start back up the learning curve of a different language? The only real way to answer is to objectively evaluate the viability of your business, not by reacting to "concerns" of a few clints.
Consider the possibility that you may be looking at the business version of an x-y problem.