In most Twitter clients, the client sends back the status ID of the status being replied to - as detailed in http://apiwiki.twitter.com/REST+API+Documentation#update This shows up on the Twitter home page as a link after the status saying 'in reply to <username>' linking to that status. It also allows viewing items as a conversation.
Currently, Twitux doesn't seem to be returning any status ID. When this happens, Twitter falls back on linking to the last status of the user being @replied to thus breaking conversation flow. 'in_reply_to_status_id' is important because when having conversations on Twitter, things may get confusing if this bit is not there.