I believe long distance relationships can work if both involved are willing to put forth the effort and dedication to making it work. If one person tries 110% to keep it going while the other just sits back and relaxes, then chances are the relationship will go nowhere. It takes two people to make a relationship work. You also need to remain faithful and truthful. If you did something wrong, don't try and hide it, it will only make things worse in the end. You have to be upfront and honest with him/her and tell them what you did, and if it's meant to be then they will take you back and you will have a second chance to make things right and regain their trust. God works in mysterious ways, but if your meant to be with your significant other, He will make sure you are on the right path.
I am currently in a long distance relationship myself and it is hard. But nobody said it was going to be easy. If your patient and are willing to wait on that special someone then it everything will be worth it in the end. You just got to believe and don't ever give up. :)