The Gale messaging system has the useful feature that you can receive messages addressed to you securely no matter where you are; you can even receive messages in multiple clients at the same time. However, the majority of Gale use is for public, unencrypted discussion. You do not receive public messages when your client is not connected; currently, users either leave a client connected all the time, or use the web-based archives to read the messages they've missed.
Since the various archives are all dynamically generated, it would be possible to provide a simple RPC or REST interface to them that a client could use to retrieve missed messages on startup. This would still miss messages marked as unloggable, but these typically only represent a small fraction of the public Gale messages.