In my experience as a contractor, the client doesn't care about the money until they do. The contractors that I have seen thrive and the times that I have thrived as a contractor is when I showed that I was there to provide value and not just "coast". Most businesses don't have time to deal with coasters until they need to cut their burn rate. If you are providing more than what you're asked you can usually stay or be first in line to return when help is required.