I've been working with my current client for the last 3 months. He brought me on at $150 per hour after he had to fire his previous contractors, and I've been cleaning up their mess ever since. I've heard of quite a few situations like this, but I'm sure that there are cheaper developers out there who are doing great work.
Demand for part-time + remote jobs seems to be pretty low in general, but I don't think my rate is the issue.
I am able to charge this much because of my experience with startups, and my open source contributions. I was an early engineer at a startup which is now worth over $500 million, and I'm currently the CTO at my own startup.
Obviously networking is one of my major weaknesses, and I need to work on that.