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)

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

857. That 'the waters were going down and abating' means that falsities started to be dispersed is clear from the actual words themselves and from what has been stated just above, at verse 3, where it is said that 'the waters receded, going back and forth', whereas in this verse it is said that 'the waters were going down and abating'. The latter as well as the former means fluctuations between truth and falsity, though the present statement means that those fluctuations were becoming less pronounced. As has been stated, during the fluctuations that follow temptation a person does not know what truth is, but as the movements gradually come to an end so the light of truth appears. The reason for this is that as long as a person's state is such, the internal man cannot function, that is, the Lord cannot function by way of the internal into the external. The internal contains remnants, which are affections for good and for truth deriving from it, which have been dealt with already. The external contains evil desires, and falsities deriving from these. As long as these external things have not been subdued and done away with, no road is open for goods and truths to pass from the internal, that is, from the Lord by way of the internal.

[2] A further purpose of temptations therefore is that the external side of a person may be subdued and so made subservient to the internal. This may become clear to anyone from the fact that as soon as a person's loves are assaulted and crushed, as they are in times of misfortune, sickness, and mental illness, his evil desires start to subside. And as they subside he begins to talk of more devout things. But as soon as he goes back to his previous state, his external man takes control again and he gives scarcely any thought to such matters. It is similar in the final hour of death when bodily things start to fade. From these considerations anyone may see what the internal man is and what the external man, also what remnants are, and how too the desires and pleasures that belong to the external man hinder the Lord's functioning by way of the internal man. From this also anyone may discern what temptations, that is, the inward pains termed the pricks of conscience, accomplish; they take place so that the external man may become subservient to the internal. The external man is made subservient solely to ensure that affections for good and truth are not hindered, halted, and stifled by evil desires and by falsities deriving from them. The subsidence of evil desires and falsities is here described by 'the waters going down and abating'.