For something to "fail" in the Bible means there is not enough understanding of truth and desire for good for someone to attain a higher spiritual state -- and possibly not enough to overcome false thoughts and the desire for evil at all. "Abate" has similar meaning but in an opposite sense, usually referring to the lessening of evil and falsity at the end of a state of temptation.

In Genesis 8:3, Deuteronomy 34:7, Judges 8:3, and Leviticus 27:18, the abating of the flood waters signifies the cessation of temptations. (Arcana Coelestia 843, 849)

(références: Arcana Coelestia 857, 5969, 6122, 8395)

5969. 'And his heart failed, for he did not believe them' means a lack of natural life and consequent lack of understanding. This is clear from the meaning of 'his heart failed' as a lack of life, and because these words have reference to 'Jacob', who represents natural good, 5965, it is a lack of natural life; and from the meaning of 'not believing' as a lack of understanding. The word consequent is used because the life that belongs to the will always precedes and that of the understanding follows; and the reason for this is that life resides solely in the will, not in the understanding except as life received from the will. This is clear from good which exists in the will and truth which exists in the understanding, in that good has life within it but not truth except as it receives it from that good. It is quite plain that what has life is always prior and what receives life from it is posterior. This explains the use of the expression 'a lack of natural life and consequent lack of understanding', meant by 'his heart failed, for he did not believe them'.