1. We don't really view ourselves as being really one with other Christians. Rather than seeing ourselves as a body, when we gather we see ourselves as individuals in a room who happen to share an individual relationship with Christ. We are all on our own journey, rather than being those who are defined decisively by the journey of Christ (from heaven to death and back!) because we are united to him. That makes the idea of a common prayer life very difficult.
2. We value spontaneity and self-expression more than discipline and mutual submission. A common prayer life requires that often we join in prayers which do not flow directly from the way we're feeling. We pray common prayers of thankfulness, including for things we have not personally enjoyed. We pray laments, suffering together even when we have not personally suffered. Because we are culturally inclined to value authenticity above all things (and that is not an entirely bad thing by any means), we tend to feel that common prayer involves some sort of hypocrisy.
3. We don't tend to pray in a way which reflects gospel blessings. We are far more likely to give thanks for particular blessings in God's providential direction of our daily lives than for his eternal blessings in Christ. That means that our prayers tend not to be about the things we have in common with one another, which makes joining in common prayer difficult.
4. Practically, common prayer usually requires a degree of formality, and we live in an informal age when formality often comes across as pomposity. We tend to think the person leading in prayer is grand-standing, even when they're not. And for people preparing to lead in prayer, the awareness that we could come across this way inhibits our praying.
5. We don't appreciate the mediation of Christ enough. We imagine we can just pick up the telephone to God at any point, and he will always be glad to hear us. We forget that we can only pray because Christ prays for us, and in so doing we also lose the corporate aspect: Christ intercedes for the church, and for us insofar as we belong to her. So as critical as individual prayer undoubtedly is, common prayer comes first - if we could only remember it.