I disagree with that, Niek. The assumption that a user "may have gone to sleep" is a bit out there, if you ask me. I think that it should be a matter of how appropriate the extra post is, taking all factors into consideration - merely re-stating the same point or revising something is something that can (and should) be handled in an edit, but additional information is most appropriate in another reply, even if that would mean double-posting.
Here are two major scenarios to illustrate:
1) In a discussion, I read initial response A and have nothing to say to it - I'm unlikely to look at the post again until there is a new post, and even then I'll likely only look at the latest unless I need a refresher of the thread up to the point. This means that if a user edits in additional information, which is perhaps something I would respond to, it either takes a fair amount of time before receiving input - or receives nothing at all.
2) This, I think, is the most important scenario. Say user posts initial Response A, and I do have something to respond with. Then, the user has additional information to add while I'm already typing my response. Unless the user adds another response, I will have no way of knowing that there was anything new - which I may wish to include a response to. If instead of merely editing their post, the user posts a new reply, I will be notified of new content before my response is posted - allowing me to revise or add information.
I think that the biggest problem is that the forum has traditionally looked down upon double-posting because of an increased "post count" for the user - which, honestly, should never have been a problem (except for when there were rewards tied to post count, which was a concept that died away quickly). Consecutive posts really do no harm to anything in the community - if anything, they show more activity, which (last I checked) was a good thing.