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That cannot be mitigated: an immitigable loss.

im·mit′i·ga·bil′i·ty n.
im·mit′i·ga·bly adv.
References in classic literature ?
From that hour of evil omen until the present, it may be,--though we know not the secret of his heart,--but it may be that no wearier and sadder man had ever sunk into the chair than this same Judge Pyncheon, whom we have just beheld so immitigably hard and resolute.
If there is any chance for experience to emerge again as a cultural force, he asserts, the immitigably vulnerable atom of the human body will be its basis--an atom that must build up social molecules with painstaking care because it has become unmoored from the hapless detritus of culture that surrounds it.
Amma is compelled to patch up the world as best he can after his mischief (Ogo concocts a host of vexatious insects and inedible fruits), but the world is now immitigably influenced by Ogo's "sign," the acacia that, like him, Davenport writes, "is incompletely made.