Note: This post does not account for the recent updates (Chapter 8 pt. 1 - Bad Behavior [V. 1.33]). It seems the new durability loss is affected by the difficulty of the stage you play and how high of a tier your equipment is.
At first I thought durability loss was directly proportional to the time one spends in a battle; however, with several experiments I determined that loss of durability, in general, is caused by how many load screens you encounter in a battle. For example: the battle called "Beginning of the Memory" (boss: Meperdu) has three stages, and thus three load screens, which include the load screen from the dock to the first stage of the battle.
Here's a summary of my findings through 18 load screens without repairing: