Intermittent "Cookies are blocked or not supported" when in client's environment with load balancer

Maybe this is more a Trellis thing rather than Bedrock, but I’m unable to make any sense out of this problem. Searched here for the specific error message and was surprised to find only 1 matching post.

The error message we’re seeing is “ERROR: Cookies are blocked or not supported by your browser. You must enable cookies to use WordPress.” and we’re mostly unable to login to the site. It does work sometimes though.

We only started having this problem when the site was moved into the client’s hosting environment, which is an Amazon Elastic Beanstalk setup with a load balancer and all the fancy trimmings. I’ve only setup this kind of thing once before but I know that this could introduce a lot of different issues.

Anybody else run into this kind of problem before? Would love to hear about it. Thanks!