There's no fight ID trigger for Mirage, it just drops the Mystile. There's no way it can loop with the Micro-Engine check either as there's no Jump to Label 4. Make sure that you've applied the patch properly or updated to the new IRO if using that. And check inventory afterwards.
I went back and made sure to use both the NT 1.5 Scene/Enemy Hotfix and NT 1.5 Flevel/Script Hotfix patches, this has fixed and changed the Mirage Fight option to Mystile drop Yes/No option and it dose add the item.
The option to add the Mystile remains every time I speak to the technician along with the micro engine key item add. I can live with it but maybe you want to look into resolving it for the mod's standing. I have noticed something else which may be related, I have an item in key items listed as -Unused- with a :O as the description. I remember I had the key to sector 5 before doing the Dark Cave side quest but had to dig it up again after since it was gone when I went to do Cid's Limit quest. I don't recall if this dose have anything to do with the Dark Cave or the Micro Engine but its the only "bug" I have really encountered so far...