No. After a given duration, Ultimate Weapon will fly off, even if the characters have not inflicted any damage. As the characters must inflict at least 80,000 HP damage (between all the fights) to force Ultimate Weapon into position for the final battle, the monster can be fought as many times as one likes. This is also true of "unleashing" Ultimate from over the lake, and even during the Disc 2 story battle in Mideel. At no point is it required that you damage Ultimate Weapon.

It's also worth noting that you can't actually battle Ultimate if he is still in the process of flying--the Highwind will merely be repelled. One can only enter into battle once Ultimate has stopped at one of the possible locations.