This problem is especially pronounced in a party situation.

In our typical party of four, we've had one of our members (who, both times, initiated the leve while none of the rest of us had it) disconnect due to a FF14 error. Each time she could go back to the crystal and initiate the quest, via leve-share, but it was still counted as failed for her, even though she logged back on while we still were IN the quest she was in.

Rather silly, imo, that she lost the leve for nothing. It was even worse because one of them was for 2000 guild marks, lol...