SHORT ANSWER: Maybe yes, maybe no.
LONG ANSWER: There really isn't always a simple answer to this question. To know whether you should break up or stay together depends on a few factors.
Do you have a strong Christian support system outside of your bf/gf?
Do you have strong same-sex friends with whom you can talk about your faith? Are you an active part of a church, youth ministry, or small group where you can learn, grow, and get support — apart from your bf/gf? Do you have Christian adults (youth leaders, family, mentors, etc.) to whom you can turn for help and advice?
My experience has been that a bf/gf is not a very good spiritual help if that's the only place you have to grow. In other words, if you are growing in your faith apart from your bf/gf, then staying together probably would work out. However, if your faith is heavily dependent on the other person, then the relationship is probably pretty unhealthy, and you both would grow more in your faith apart from one another.
Are you intentional about giving your faith the care it needs? Do you have a specific idea of what's wrong or is it just a general, disatisfied "I want to grow" feeling?
Somebody who is taking specific steps to grow (reading a book, joining a Bible study, journaling your thoughts, etc.) will do much better in a relationship than the person who doesn't have a plan. If you only have vague ideas for improving your faith, it probably won't happen. To make matters worse, all the emotional and physical distractions of dating will just draw your attention away from improving your faith.
Are you actively dealing with the sin in your life and relationship?
Dissatisfaction in a dating relationship (and even in our relationship with God) often has it's root in sin. You might tell yourself that a particular behavior is okay, but your soul knows better and aches over the distance from God that sin creates.
This doesn't necessarily mean that your relationship has to be sinless, but it does mean that you're actively dealing with your sin through confession & repentance, accountability partners, and getting extra help where you need it. If you and your bf/gf are unable or unwilling to stop an obviously sinful behavior, then you probably need some time apart to allow God to heal and strengthen you.
THE BOTTOM LINE
If you have a strong Christian support system, are intentional about addressing areas of your faith, and are actively dealing with sin in your life, then I would say stay together. Just enlist some help on your faith from someone other than your bf/gf.
If you fall short on all three or even two of these, then you need to seriously consider breaking up in order for each of you to work on your own relationships with God. Being in a romantic relationship probably isn't helping you at all right now and definitely won't in the future.
MY BEST SUGGESTION
Trust your gut. A lot of times when somebody asks this question, their gut (and possibly the Holy Spirit) is telling them they should break up, but their heart is saying no because they don't want to lose the other person. So, listen to that voice inside you and remember that breakups aren't always forever. You never know what God might have in store for you when you focus on getting your relationship with Him healthy first.