I have some indication that messages sent to me in the menu screen has been lost. Has this been registered before? What if one exits the game while it is communicating with the server? Will the server register any messages in que as sent?

All such messages are immediately deleted on Game Server as soon Server gets a confirmation the messages were received by player.

After that, the messages exist only in player data. If a player uninstalls MAN2 or MAN2 data is corrupted messages are lost.

So what you are saying is that you HAVE to press "discard" or "reply" to delete the messages from the server?

No, message is deleted from server immediately as soon as you get it from server to your computer. When you press "discard" or "reply" you delete this message from your computer.