Short answer: me :)
I was working on my part-time project for about 3 - 3,5 months until 1.0 release, investing about 10h/week. After the release, I worked on it for about 6 more months before quitting my day job (more on this here).
I used that time for the obvious things:
• making the product better
• increasing income and...
• saving it for the time after I quit
My advices for working part-time:
• choose a simple project
• choose a project that's interesting to you
• choose the market, niche and your competition wisely
• release early to receive feedback and hopefully some money - each will validate your idea and can motivate you to continue working on it
• if you get positive feedback and some money your idea is validated and you're already closer to success :)
I learned that from my 2 projects.
• Weight training assistant for Nokia phones
Fairly simple project, interesting to me. Market pros: does not require much upfront investment. Market cons: very fragmented (many devices with different capabilities), hard to reach (marketing difficult for low-price-point apps) and with many obstacles (for the potential costumer - from app download and installation - to payment). I was working on the project too long before the first release, just to find out that it won't sell ;)
The result: failure.
• Time tracking app for iPhone
Fairly simple project (well defined, using good iPhone SDK and standard frameworks). Interesting to me personally (eating my own dog food). Market pros: big, homogeneous, does not require much upfront investment. Market cons: very competitive, very young.
I released early, got some encouraging feedback and started earning from release day one.
Right now, about 11 months after 1.0 release and 5 months after quitting, I'm starting to earn more than in my ex-day-job. Will this trend continue? That remains to be seen, but...
the result: closer to success :)