I did freelancing (web, then iOS) for 8+ years based in the US, but for companies (large and small) around the world. I rarely worked with companies in my local area. The problem is thinking of the clients as "employers".
If you think of them as just clients and you have a lot of inbound leads (built up by word of mouth over time), then you can choose the projects that interest you.
In my experience, projects ranged from 6 weeks to 6+ months, but I almost always had multiple projects in various stages happening at the same time. There were often a couple other freelancers on the project, coordinated by a project manager. It's useful to work with or through a design agency or "interactive" agency (as they were called 10 years ago). The key is to manage the entire project from start to finish for the client. The worst problem is clients who don't deliver content/approvals/etc, so you need someone focused on bugging them.
I also usually set a per-project price, not hourly. I hated tracking hours and it didn't give me the motivation to get stuff done faster. A fixed price also forces everyone to agree on a detailed spec up front. Add a little padding into your price, so you you can be kind about implementing the inevitable changes.
tldr; Yes, it's totally possible to make a living doing freelance development, all from home (or anywhere you want).