How to handle pricing disagreements?

Began negotiating a new contract with one of our largest clients and users. Their three year deal is coming to an end. Originally signed on as one of bigger clients, with annual fee around $100k.

The product has changed completely since then. Feedback from this client is incredibly positive, relationship is great, usage is huge, and we mostly treated them like royalty during the term - doing many things out of scope due to their comparatively high fee.

I proposed a new three year deal at a 20% increase, which was perfectly reasonable based on new features, inflation, usage, service etc.

Instead, they’ve come back threatening to find another provider and have pointed to a three year old agreement with archaic pricing to justify that they don’t use little bits of the platform and therefore it should be way cheaper.

How do you deal with this kind of thing? Usually our clients are receptive to reasonable price increases, but these guys have shot back quickly and it’s taken us all by surprise. We don’t want to have put massive amounts of work into a three year engagement, only for the annual contract value to decrease.