A mercenary falls after losing all health in battle. A critical hit or a blow that exceeds their remaining health by a large margin can trigger a death check; survivors recover from their injuries.
Check the battle result for injuries and deaths among fallen mercenaries. After returning, review injury recovery time under "Mercs" and visit "Records" for the records of those who left the guild.
Check fatigue and defensive equipment before risking your main party. Improving the Infirmary reduces the chance of death on a fatal fall, with a risk of 1% at its highest level.