I had a client who was quite profitable during the web development phase but wasn't worth my time to keep website updates. A professional would realize you cannot just serve your client for the fat dollars and leave them twisting in the breeze for the thin dollars. It's very unethical. The client is depending on you. Your instinct to not serve them stems from accounting concerns, but you cannot act on that impluse.
Larger issues are at stake.
You have already made significant gains on the initial development. Your first action should be to reconcile your thoughts. Your client can be a valuable asset, either through future re-designs or from just passing your name along at the next Rotary meeting. Professionally, you need to discuss the matter with your client. Updates have no economy of time in that you are not already in the site, borrowing templates and lines of code for re-use.