People give up their faith because;
1) They forget how important our goal is - to save ourselves from spending eternity in Hell. When we lose sight on how wonderful Heaven is going to be, it's easy to just want to give up. But we have to remember that Heaven is better than anything we could ever imagine - with no pain and no sadness. Paul tells us in Philippians 3 to "Forget the things that are behind and press on to the things that lie ahead."
2) People want to give up because they don't receive enough encouragement from others. As Christians, we need to make sure that we're uplifting our fellow brethren. Hebrews 10 tells us to exhort and encourage one another and Hebrews 3 tells us that we need to do this daily. It's important for us to do this for one another.
3) People want to give up because they forget the teaching of God's word. But we should remind ourselves of scriptures like Phil. 4:13 " I can do all things through Christ who strengthens me..." and 1 Peter 5:7 "Cast all your anxiety upon Him because He cares for you."
On our race to the finish line, it's important for us to NEVER give up.