KUALA LUMPUR, Malaysia—Back-to-back disasters at Malaysia Airlines have had a devastating effect on the carrier's flight attendants, sapping morale and leaving some of them too distraught to fly.

Since March 8, 21 flight attendants and six pilots have died, first when Flight 370 disappeared in an agonizing mystery, and then when Flight 17 was shot down Thursday over a conflict-torn area of Ukraine.

The...