Messages you've sent in the last 48 hours will appear in your sent items folder. All messages with replies will be shown in your main messages list. This is to reduce clutter in your mailbox so you can focus on current conversations.
Your messages won't be removed from the other person's inbox and they'll still be able to reply at any time.
How will I know if I have contacted someone already?
If you visit the profile of someone you have already sent a message to, you'll be able to see this when you look at the message and wave buttons. Pressing the message button will let you view your previous conversation.