I've recently made a transition from full-time work to sparse, part-time freelancing, which I deem successful, but may not be by others' criteria. The parameters of my freelancing are undoubtedly much different from yours, but perhaps my experience is still of use.
Up until May 2014, I was working FT at a small non-profit (government-supported) consulting firm in the medical devices space. At this point I had about a decade of progressive development experience and more than half of that in the medical space.
I wasn't totally happy at that position for various reasons and, for some time, I had been interested in having more time to work on my own projects. Part-time work was what I thought I needed, but no employers were interested in that kind of arrangement.
Also significant is that in April 2014, our first child was born and I knew that I wanted to be an involved parent. So as my son's due date came closer, I investigated freelancing as an option.
Another factor that is important in my case is that due to my previous employment and my family's relatively frugal means of living, we are doing OK financially. We live in a medium-sized city in Canada where living costs are lower tha your bigger tech hubs. I knew that I could go a year or more with almost no income that we'd still be fine. I've come to realize that this is a blessing and a curse at the same time though ;)
To be honest, some things just fell into place for me. One of the clients that I was the lead on at my day job was someone I knew that I could talk to openly and when I told them that I would be leaving, they showed immediate interest in retaining my services.
My employer was fairly shocked at my leaving. I was (and I try to say this as modestly as possible) the most productive and reliable developer there and also the one trusted most with customer relationships. I gave them plenty of notice (6 weeks) and we left on very good terms.
Here's the kicker, my old employer is now my #1 client. I am essentially a subcontractor to them. I make about 1.75x what I did as a FT'er on an hourly basis doing my old job for them, but I have the ability to set my hours, workload, and decide which projects I take on. It's almost funny to me because if they had offered me reduced hours and similarly reduced pay in the past, I probably would have taken it. I charge them a bit less than other clients, because they take the pain of finding new customers out of the equation for me.
All this said, I bill about 50 hours a month. I could bill more (take on more work), but that isn't my objective. The other time I spend working on my startup and I spend an above average amount of time at home, being a dad. This is exactly the arrangement I was looking for and I couldn't be happier with life these days.
This won't last forever. That's why I've got the startup in the works and also I know that, should I ever need, I have a reasonable number of contacts in my city to get another job (and I'm sure my old job would still be available should I choose to return).