What does the Bible say about 'giving up' in general?
“Wherefore seeing we also are compassed about with so great a cloud of witnesses, let us lay aside every weight, and the sin which doth so easily beset [us], and let us run with patience the race that is set before us, Looking unto Jesus the author and finisher of [our] faith; who for the joy that was set before him endured the cross, despising the shame, and is set down at the right hand of the throne of God. For consider him that endured such contradiction of sinners against himself, lest ye be wearied and faint in your minds. Ye have not yet resisted unto blood, striving against sin. And ye have forgotten the exhortation which speaketh unto you as unto children, My son, despise not thou the chastening of the Lord, nor faint when thou art rebuked of him.” (Hebrews 12:1-5)
“And he spake a parable unto them to this end, that men ought always to pray, and not to faint; Saying, There was in a city a judge, which feared not God, neither regarded man: And there was a widow in that city; and she came unto him, saying, Avenge me of mine adversary. And he would not for a while: but afterward he said within himself, Though I fear not God, nor regard man; Yet because this widow troubleth me, I will avenge her, lest by her continual coming she weary me. And the Lord said, Hear what the unjust judge saith.” (Luke 18:1-6)
“And let us not be weary in well doing: for in due season we shall reap, if we faint not. As we have therefore opportunity, let us do good unto all [men], especially unto them who are of the household of faith.” (Galatians 6:9-10)
These are all about not giving up in spiritual things. However, the principle still applies; if we want to succeed in something we must persist.