Yeah it should persist while offline. Though 1 thing I thought up later on which might be a problem is that if everyone has trade posts up, it could potentially be many pages of trades to sift through... and it could be even harder to search for rares. I guess u could add some sort of filter to excludes posts that don't have items with certain stats though.Sounds similar to what I had in mind. I assume items up for trade would be visible even when the seller isn't online, correct?
Let me repost my reply to JEB90's post from another thread here as well. In my reply I touched upon the possibility of keeping the AH, while improving the drops and why I think that wouldn't help things:
An alternate setup could be an interface where u can list all the items u have for trade, and also where u can setup a wants list. Then to do the trade... when person A sees that person B has something he is after, A can offer a particular trade to B who would then get a confirmation window. B can accept, decline, counter-offer, or msg the other person to discuss the trade. Basically what would normally happen on trade forums like this, except with a proper in-game interface.