It doesnt save them becuase your not editing the historical list, your creating a new message, which u then abandoned by pressing the down arrow. you can do one of two things to fix this problem (id suggest number 2)
(1) highlight the whole message your editing and press ctrl-x, type your short message in, press enter, then press ctrl-v, previous message reappears
(2) right click over editbox, select options, tick enable editbox, click ok, now you have two edit boxes, one you can scroll back in and edit previous messages from and one for short instant messages you might want to send