A weakness or disability, especially due to old age, is called an infirmity.

The noun infirmity, when used alone, is generally understood to mean physical frailty. If you want to imply mental weakness or some other disability, then use an adjective for clarity, as in this example: "His mental infirmity was caused by an early onset of Alzheimer's disease." Don't confuse infirmity with infirmary. The latter is a place where the sick and infirm go to recover: "Because of her infirmity, she often ended up being seen by doctors at the infirmary."

Definitions of infirmity
  1. noun
    the state of being weak in health or body (especially from old age)
    synonyms: debility, feebleness, frailness, frailty, valetudinarianism
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    asthenia, astheny
    an abnormal loss of strength
    cachexia, cachexy, wasting
    any general reduction in vitality and strength of body and mind resulting from a debilitating chronic disease
    type of:
    softness, unfitness
    poor physical condition; being out of shape or out of condition (as from a life of ease and luxury)
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