This applies to every aspect of our Christian journey except for one: we SHOULD give up depending on our own human abilities in our walk of faith: “….that we may not be trusting on ourselves, but on God….” (2 Corinthians 1:9).
Regarding our failures and multiple sins, I always remember the words of William Law in one of his writings (I cannot remember which one as I have read so many of his works). He STRONGLY emphasized that as long as we have a breath to breathe, we should never give up looking to God and Christ Jesus for forgiveness (as well as help), no matter how severe our past and most recent sins may be….and if it is done with a sincere and heart felt repentance.
The absolute horrendous sins committed by King David with Bathsheba and Uriah are an excellent example of just how merciful God and Christ Jesus can be, as discussed further in the Post “David’s Heinous Sin vs God’s Mercy”.
Regarding our efforts to Spiritually grow and come into a more personal and deeper relationship with God and Christ Jesus, the following two examples serve to clearly illustrate this truth of never giving up.
The first is the author of the of the book THE CLOUD OF UNKNOWING ( http://www.ccel.org/ccel/anonymous2/cloud.html ). This Christian was unceasingly seeking a closer relationship with God and the Lord with (literally) almost moment by moment supplication to Them during every waking hour. And yet, this person was constantly met with no response from Them. This Christian went on to say that at times it was as if a steel, locked door (or similar words) had been placed between her/his access to the Father and Jesus.
Nevertheless, this believer NEVER,EVER gave up, and eventually reached amazing Spiritual heights.
The second example is Brother Lawrence as revealed in his book PRACTICING THE PRESENCE OF GOD (please reference the Post by this same title). During his efforts to become closer to God and the Lord, he wrote that “It seemed to me that all creatures, reason, and God Himself were against me and faith alone for me.”
And yet, he persisted and eventually came to experience the astonishing and ‘supernatural’ presence with the Father and Christ Jesus as described in his book (http://www.gutenberg.org/cache/epub/5657/pg5657.html).
We can say NEVER because He says NEVER: “I will NEVER desert you, NOR will I EVER forsake you”. (Hebrews 13:5)
All in best, in Him.