It's April 2015 and we started receiving some calls that our servers have vanished. Not good. Investigation reveals that a change in Google's DNS handling means, as far as Google's DNS servers are concerned, our servers don't exist. And we're not the only ones having this problem - it's common to systems using CNAME aliases to Amazon AWS ELB (Load Balancers).
Here's how to determine if this problem is affecting you and how to resolve it - short term and long term.