My friend Dave Thair pointed me towards Meme-nto [2008: link now dead], a concept site which
examines how internet discussion is governed by impermanence. In simple terms, it's a messageboard where only the last three messages are displayed - others are lost into the ether. This is meant to mimic what happens in offline conversations, where newcomers have no record of what was said previously, and just have to figure out what the topic is and join in.
Interesting idea, but I think that this already happens to an extent within online communities. E-mail lists, one of the oldest forms of many-to-many internet communication, are a good example. You only start to receive messages after you join, so usually this does require a period of working out the topics and tone of conversations before joining in ('lurking'). To an extent this applies to many other forms of online community - messageboards, usenet, chatrooms, even weblogs - where there are archives, they are either seldom read or on a low retention. It's a common complaint that people don't read the backlog first before posting ('read the FAQ!').
I think a bigger difference between online and offline conversations is not permanence, but time scale. Whereas conversations down the pub take place in real time, many forms of online communication have hours, days, or weeks between replies. It's because of this that retention is needed - if you came back online to discover that the replies to your message had been deleted, communication would break down. It would be the offline equivalent of unread replies to your letters being binned if you didn't read them quick enough.