Kell, one always has a right to work for a rate one needs to survive. One has the right to renegotiate. "honor" does no good if the results sends you to bankruptcy.

The client certainly has a right to take their business elsewhere but they may still find your offer reasonable.

I've had somewhat similar circumstances. In my case I had a project with a budget and a defined number of hours of work (something I ALWAYS do in a contract). There was no final delivery date though. Nearly 9 months later the client wanted to book for final revisions. At that point my rate had gone up. I was not about to push out higher paying clients to complete this lower paying client. I gave the client two options. They can pay my new higher rate and I could book them at the first available date or they could pay the original rate and would have to wait until I had an open date in my schedule or otherwise finish it catch as catch can (in other words, when I found the time). They opted the for the latter so it took another 5 months for the project to be finished. They were very genuinely happy when I sent them the DVD on the morning of their presentation.

Your job is to do what's best for YOU and YOUR BUSINESS.

One thing you can do is take on work on a "contingency" basis. The client is told that as part of the lower rate their work can be set aside for higher paying work. This would allow you to take on lower paying jobs and not lose higher paying jobs when they happen. You SHOULD ACTIVELY seek higher paying work though and you MUST keep to your commitment of pushing aside such lower paying work. If someone has a RUSH or HARD DEADLINE they must pay for that. Still NEVER GO BELOW would you need to cover ALL YOUR LIFE AND BUSINESS EXPENSES. That is the RULE of survival.