It is possible to resend a message that's in a DONE status.  I'm not saying that it's a good idea, just that it's possible.  Here's how to do it in PeopleTools versions prior to 8.48:

I don't consider myself an Integration Broker expert.  Far from it.  I can get messages to fly from one PeopleSoft instance to another, I can write a transformation if pressed, and I can get messages that are stuck in a "New" status working again.  So I thought I'd go out on a limb here and pass along my mental model of how I visualize Integration Broker working.  If you're an expert, you might find this article simplistic and inaccurate at times and I'm hoping you'll speak up and let me know of the glaring problems.  But if you're a new to IB or trying to support somebody else's integrations you might find something in here useful.

If you think about it, any messaging system needs some basic building blocks to work.  Think about an e-mail system.  You have a Sender and a Recipient.  E-mail addresses are made up of a user (the part before the @ sign) and a domain (the part after the @ sign).  You have an e-mail server that routes the e-mail to the Recipient’s domain.  A server on the Recipient’s domain then gets it to the recipient’s inbox.  When the Recipient opens it, a Return Receipt e-mail might be generated back to the Sender as an acknowledgement.

Integration Broker follows a lot of these same rules.  But since its messages are generated and consumed by machines, things are more structured.