I had the quest on my MRD. I decided I instead wanted to do the quest on my DRG, so I abandoned it on my MRD. After abandoning it I could not get the quest back, it just didn't show up on the NPC that gives it out. I tried switching back to MRD to see if I could grab it with that class again, but it still was not there. So for 3 days now I have been unable to restart the relic reborn quest, and I am falling behind my FC since they are getting ready to raid Coil.