Perpetual sounds like another way of saying unlimited. Every story I have ever read involving an unlimited contract involved bleeding the company that agreed to provide unlimited service.
People who bought unlimited airline flights for life basically live on airplanes. They soak the airlines for all they can get.
I have seen stories of small shops that died largely due to agreeing to give unlimited service to a single client for a fixed fee.
They are asking you to enter a contract where they pay you one time and then service them forever. If that doesn't sound like a deal with the devil, maybe read up on what a bad deal slavery typically is.
A quick skim of articles comparing perpetual and SAAS licensing suggest SAAS is more lucrative. If he's barely making a profit now, this sounds like it only gets worse.
I based my assessment of the scenario in part on this being his largest client. Large companies routinely screw over small ones. It is par for the course. You can basically assume that if a big company wants it, you are likely to lose your shirt if you are overly cooperative with their agenda. They are looking out for number one. They are not looking out for you.
It sounds like he didn’t price it right. SaaS is more profitable in general because you own the customers data, guaranteeing renewals, and it’s cheaper to support an app than support a customer on Amazon.
I made a lot of money selling a little application to an enterprise that did some data transformation. That enterprises policies would have prevented them from buying a SaaS from me.