Have a failover DNS provider. Amazon uses Dyn, but also has UltraDNS as a backup, and it's obviously still up. Twitter vs Amazon:
host -t ns twitter.com: ns3.p34.dynect.net, ns4.p34.dynect.net, ns1.p34.dynect.net, ns2.p34.dynect.net.
host -t ns amazon.com: ns3.p31.dynect.net, ns4.p31.dynect.net, ns2.p31.dynect.net, pdns6.ultradns.co.uk, pdns1.ultradns.net, ns1.p31.dynect.net.