It's just like when you are taking a shower and an idea hits you, it's because you aren't focusing on work and you are in complete silence. You need time to relax, recharge, and recover. Believe me I only learned this through experience, but you need a break every now and then.
I was reading this article from the founder of Kayak earlier today: http://onstartups.com/tabid/3339/bid/12604/Startup-Insights-... and he mentioned something interesting. Despite being a travel startup, he avoids hiring people from the travel industry. I believe that's because he sees value in having people with different modes of thinking.
And in a way, that's kind of what a hobby does for you. It puts you into a different mode of thinking, which can come back and benefit your startup. :)
Just my $0.02.
http://www.ted.com/index.php/talks/stefan_sagmeister_the_pow...