I've had this issue before. When running WordPress (or other PHP scripts) behind Amazon's EC2 Load Balancer, the scripts do not realize they are being ran on the https:// protocol and results in issues such as endless redirect loops, and HTTPS warnings ("Some content on this page is being requested in a non-secure way...").
I found a solution here, but requires modifying WordPress core, which is no good for updatability: https://wordpress.org/support/topic/when-behind-amazon-web-services-elastic-load-balancer-causes-endless-redirect
Is there a way to fix this without modifying WordPress core? I am using Apache 2.2.