I know what I did to avoid such problems and further to negate DDOS attacks was to switch to a DNS provider that has huge footprint so that the TTL is very for refresh. Not sure if it a great plan. But being able to have domain resolve to new IP addresses in about 1 minute. Which is pretty fast.Totally agree. Unless you're one of the big boys with your own data centers, or have some very special needs, there's no reason to host your own DNS server and plenty of reasons not to. It does not need to be handled by the same provider hosting your web site/web app.
BTW - can you share what DNS provider you are using?
"Amazon Route 53 is a highly available and scalable cloud Domain Name System (DNS) web service"