After renaming an EC2 instance behind an AWS Elastic Load Balancer (ELB), I noticed that the https listener was timing out. I had multiple ELBs pointing to the same instance because we terminate SSL on each ELB (one ELB per apache virtual host).
This is our setup but its not certain what the actual conditions are to experience this bug.
The solution was to delete the https listener on each ELB and recreate it.
Https was immediately accessible after doing this.