By default, a DB instance is not publicly accessible (not bound with an EIP) after being created. You can bind an EIP to the DB instance for public accessibility and can unbind the EIP from the DB instance as required.
To ensure that the database can be accessed, the security group used by the database must have the permission to access the database port. For example, if the database port is 8635, ensure that the security group has the permission to access port 8635.
This function is currently unavailable for some existing DB instances because the connection IP addresses were created in a way that does not support binding EIPs.
To unbind the EIP from the DB instance, see Unbinding an EIP.
To bind an EIP to the DB instance again, see Binding an EIP.