We press on because Phillipians 3:14-16 tells us to "press on toward the goal to win the prize for which God has called us heavenward in Christ Jesus".
There are some people in my church who believe that once we are saved, we are always saved, and that salvation requires no effort on our part. The view is that because we are predestined, nothing can pluck us out of the Lord's hands. As we are chosen, then we are eternally secure.
There are others in my church who take a different view. They will state that believers have the freewill to choose whether or not they will continue abide in Christ, that we have to choose to take up our cross daily and follow Him, that any tree that does not bear fruit will be cut down. Some Christians believe that some serious sins, particularly "mortal" sins, if not repented of, will result in the believer falling from a state of grace.
I do believe that once we become Christians, the Lord does not give up on us that easily. He is very faithful to us and when we fall into sin, He picks us up and encourages us to walk on with Him. Whether we are pre-destined to have faith, I do not really know for certain although my church officially and historically placed a major emphasis on this doctrine in its 39 Articles. All I do know for certain is that I have strayed from the path many times and have always felt the Lord bringing me back on track.