Normally when you lost a mission, it is gone, and it is marked with an "X".
Currently, I lost a mission when trying to get Bahamut Science Exo. Thankfully I can try it again, but all map is changed.
I am a big advocate of randomizing, and I really enjoy not knowing what to do next etc, but if there is one Bahamut Science Exo in the city, then should not map be the same each time you try to get it? Or should I think like, "ohhh robots now are aware of my evil plans so they just relocated the exo." To make myself clearer I am not against this because it makes the game harder, I am against since it does not make that much sense in terms of 'lore'.
