Current condition (as described by Bb Open LMS support): "Snap personal dashboard display users recent messages from last 12 weeks. If messages have not been read users will see unread notification. They are not removed from recent messages when user has read the message."
Messages, once read, are no longer displayed on the "My Courses" page under "Messages" and let the age of the messages displayed (e.g., last 12 weeks) be an admin configurable duration.
Second Best: Messages, once read, are displayed is a less bold font face, following similar convention used in messaging applications elsewhere.