I just tried to make my domain name point to the elastic beanstalk environment that I have been working on and it has just reset all of the theme and plugin data on the instance. This has happened once before, I think it might have to do with rebooting the instance from EC2.
Amazon has instructions for deploying WordPress on Elastic Beanstalk. The part that will prevent your problem is the section "Enable WordPress to Store Assets in Amazon S3".
You have to install the "W3 Total Cache" plugin in WordPress and configure it to use "Amazon Simple Storage Service S3". When you have done that, plugins and themes will no longer be stored locally on the EB instance. They will be stored more permanently on S3.
It sounds like right now your plugins and themes (assets) are stored locally on your web server. EB may destroy and redeploy your servers at any time which erases your customizations.