気を落(とす means to lose heart or become discouraged after bad news, a setback, or a disappointment.
Literal Meaning
This expression literally translates as “to drop one’s spirit/energy”. The word 気( represents one’s spirit, energy, or mood, while 落(とす means to drop or let fall.
Usage Notes
The phrase often appears as 気を落とさないで, “don’t be discouraged” or “cheer up”, when comforting someone who feels defeated.