Nope. I've changed my residency from UK, to NZ, to Canada in the last 1.5 years, and have used my ESTA as recently as last week, and it's fine. It's tied solely to your passport/citizenship. I was open about my changes at the border, my Canadian permit is even in my passport, and they were totally fine.
Of course, once your ESTA is more than two years old (as mine will be in November) you'll have to apply for a new one :/
It seems weird that we don't need visas, but we have to pay $US14 for a visa-waiver. Sounds like a visa to me (rant) :)