dotage \DOH-tij\ (noun) - Feebleness of mind due to old age; senility.

"'So, what are you up to in your dotage?' Dotage! He realized he absolutely loathed this word; he refused to be in a dotage -- in any way, shape, or form." -- Jan Karon, 'Light from Heaven'

Dotage comes from the verb to dote, "to be weak-minded, silly, or foolish; to have the intellect impaired, especially by old age," from Middle English doten. One who is in his or her dotage is a dotard.