I've played PS2 (and others) many times. I have no direct proof of what I'm going to tell you but it is based on experience. Shir's level definitely seems to have an effect on what she steals. (i.e. she must be at least lvl 10 to get the visiphone from the tower). However, as the mod said, she will steal stuff corresponding to the type of shop she is in. I normally level all the characters (because it's fun) and when Shir is with me; I stop in various towns that are near by so she can steal at every single level she attains. I believe it is totally random when she disappears. Sometimes it's immediate, sometimes it feels like it's totally "off". But the best things I've nailed early on is JWL Crown or Fire Staff. As I said, other stuff seems to come later. (Ummm.. I'm pretty sure she did nail a star mist and moon dew early once or twice???) That was definitely welcome. The most expensive things I ever saw include a Pulse Cannon, Lac Dagger, Lacn Mace from Dezo; but she was way up in level. She got Shuneboots before I could afford them (or at least wanted to spend on them) like mid-game and that was excellent. Keep at it. I had forgotten about that frustrating but enjoyable part of the game. A Fire Staff is awesome if she steals one early for you. It's as good as a laser knife if not better for Amy.
Good luck man!