I fought with this for too long before discovering the solution. I was getting a pretty standard connection error (as seen below). I had double-checked permissions, even going to far as to give full S3 permissions to my IAM user just to see if it would work, double-checking outbound firewall ports, etc. Everything checked out, but it still errored out.
My solution: My bucket name had dots in the name. S3
doesn’t prevent this, but apparently it causes some sort of issue with
the SSL connection. Create a new bucket with no dots, if you used them,
and it will likely take care of your issue.