existential threat; life-or-death crisis
A crisis that threatens the very existence or survival of a person, organization, or entity. Often used in formal or serious contexts.
The company is facing an existential threat.
Climate change is a life-or-death crisis for humanity.
危機 is a general crisis or danger, while 存亡の危機 specifically emphasizes a threat to existence or survival.
存亡 means 'existence or demise'; 存亡の危機 combines it with 危機 to form a set phrase for an existential crisis.
Compound of 存亡 (sonbō, 'existence or demise') + の (no, possessive particle) + 危機 (kiki, 'crisis'). The phrase is a straightforward combination of its parts.