Some networks have this. It's called MemoServ, but it only activates on private messages. Logging channels would be insane, though there are many IRC logging projects out there on google. You can opt your channel into the service and have the logs available to all on the web.
edit: as I've just seen the topic from feature suggestions I think it's important to point out that none of the above solutions can be implemented by mIRC, these are all (and must all be) server-side solutions. For mIRC to know about what happens on a channel 24/7 it would need to be connected 24/7, defeating the purpose of "offline messages".
