I've never seen an external IP address for an EC2 box change, I don't believe they do. They are typically part of the hostname and it would be strange to have amazon change this at random points in time. Elastic IP is good if you want to change a server a domain points to without having to wait for DNS propagation.
I just confirmed that I can access your AMI in the US East region. Be aware, however, that AMIs are region specific and thus your AMI cannot be found or used in any other region (such as US West).