What's important is that you treat the DNS management aspect of your business as a proper thing to be managed by itself. Whether you host it yourself, or contract it out to a service that specifically does this for you is a matter of risk tolerance and budget.

A common setup is a private nameserver that you host yourself, wherever, that isn't publicly used. You then contract UltraDNS/Neustar or their brethren and set them up as your public servers, doing zone transfers from your private ones. You get the advantages of direct management of your zones, and the global scale infrastructure needed to largely eliminate nameserver issues.