In the New Testament, my favorite passage on this theme is "Therefore since we are surrounded by such a great cloud of witnesses, let us throw off everything that hinders and the sin that so easily entangles, and let us run with perseverance the race marked out for us. Let us fix our eyes on Jesus, the author and perfercter of our faith," (Heb 12:1-2). One could argue that the author had in mind a group of individuals (stress on individual walks), but I think the stress is on the group as a whole not falling away.
This implies what Paul made clear elsewhere, "Brothers, if someone is caught in a sin, you who are spiritual should restore him gently. But watch yourself, or you also may be tempted. Carry each other's burdens, and in this way you will fulfill the law of Christ," namely to love one another (Gal 6:1-2). The Greek pronoun for "you" in this context is plural. So in the south today it could be translated "ya'll."
The church is supposed to be a body in which we do life together, pursuing God. We are on a marathon race together, and the goal is not to be the first to cross the finish line leaving all of our brothers and sisters in the dust. Instead, as Bunyan envisioned, the goal is to get all of us home to Jesus in the Celestial City through the power of His Spirit in us as we carry each other. We can sin. We can succeed. Consider too Paul's letters to churches, rebuking whole churches for the sins of individuals within the church. Corinth was held responsible for the collective attitude towards one man's gross sin (1 Cor 5:1-2). Why? Because there is a communal aspect in Scripture that we in the hyper-individualistic west ignore. It's one of the reasons discipleship is often lacking in our country. We all want to be heroes, but God designed the church to be a team.
It is good for us to want to grow individually closer to God. Each of us, individually must seek to live pure and holy lives, devoted to the glory and righteousness of God. So, Paul told the Roman Christians, "Brothers, we have an obligation - but it is not to the sinful nature, to live according to it. For if you live according to the sinful nature, you will die; but if by the Spirit you put to death the misdeeds of the body, you will live," (Rom 8:12-13). But, don't miss it. We do this together. We put sin to death as we fight each day of our lives against our own sin and with the help of our brothers and sisters. Therefore we must pray for one another, talk to one another, confess our sins to one another, hold each other accountable, laugh together, cry together, meet together, serve one another, love one another (desire and work towards God's best for each other), and do this until we all get home. James said, "confess your sins to each other and pray for each other so that you may be healed," (Jam 5:16).
At one point in my walk, God blessed my heart with the conviction that I really needed help and so I went for Christian counseling, which is simply focused discipleship. It was wonderful! And God used my focused time with a wise brother to help me defeat sin and grow in purity. As we continue to want to grow in our personal walks with Christ, I think it is important for us to ask God: "Who can I ask to carry me?" In ministry especially, it's too easy to assume our job is simply to carry others. But, Paul rebuked Peter once (Gal 2:11-12), and asked for prayer often (e.g. Eph 6:19). Even Jesus asked his closest friends to stay awake and pray with him in Gethsemane (Matt 26:36-38). Likewise, we need each other. Most of us know this, but I encourage any Christian to be more open and more interested in biblical friendships than ever before. Be transparent, helpful, prayerful, and faithful through the power of Christ. Pursue both your personal walk with Christ and our communal walk with Christ.