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Definition of failing : 1. A failing short; a becoming deficient; failure; deficiency; imperfection; weakness; lapse; fault; infirmity; as, a mental failing.
2. of Fail
3. The act of becoming insolvent of bankrupt.

Synonyms:

failed, weak point, flunk, declining, help, unsuccessful, dying, regressive, fault, retrogressive, foible, deteriorating, weakness, regressing, helplessness, faint, aging, weak, better, frailty, feeble, retrograde, infirmity, impuissance, unsatisfactory, shortcoming

falling, floundering, blundering, stumbling, flopping, collapsing, busting, losing, faltering, flunking

forgetting, neglecting, overlooking, ignoring, disregarding

Usage examples:

• The usual anxiety at the camp was the question of water supply; I had found so little where I had been, and the water here was failing rapidly every day. - "Australia Twice Traversed, The Romance of Exploration Australia Twice Traversed. The Romance Of Exploration, Being A Narrative Compiled From The Journals Of Five Exploring Expeditions Into And Through Central South Australia, And Western Australia, From 1", Ernest Giles.
• Any player failing to catch the ball, or catching it while seated, changes places with the thrower instead of being out of the game, as when the teacher throws. - "Games for the Playground, Home, School and Gymnasium", Jessie H. Bancroft.
• At the close of his year at Prairieville, his failing health compelled him to leave the work. - "Thirty Years in the Itinerancy", Wesson Gage Miller.