I spun up two RDS instances in the same VPC. Both are postgresql.
While the m4.xlarge one has multi-AZ enabled and is encrypted. The t2.micro has either. That is the only difference between the two instances. It is strange that t2.micro instance can be stopped but m4.xlarge can't. The "stop" option is grayed out for m4.xlarge. Why can't I stop this one? Does it have to do with the multi-AZ thing?
You can't stop a DB instance that is in a Multi-AZ deployment.
http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_StopInstance.html
Modify the instance so that it is no longer Multi-AZ. After this modification is complete, you should be able to stop it. You can switch it back to being Multi-AZ after it is restarted.