"she just keeps on moving further away from me..." That pretty much says it all! The answer to your question is NO! The relationship cannot "work out" unless (both people) want it to. You see her as being "the girl of your dreams" BUT she clearly does not see you as being "the man of her dreams".
Seeing someone every other week is usually not a "deal breaker" for most long distance relationships when (both people are in love). Some people don't see their significant other for much longer stretches of time, especially those involving people in the military. I suspect she is simply burned out on the relationship itself or has an eye out for a potential new relationship with someone else. You did not mention either one of your ages. It's very possible that she is too young or is not ready to settle down. For whatever reason she does not see you as being "Mr. Right"
Five months of dating is usually still considered the "infatuation phase" for most relationships. And if you are only seeing her every other week then your "actual time" together is more like 2 1/2 months! I would not waste time and energy trying to convince someone to stick with me who did not want to be with me. In order for her to be "the one" she has to see you as being "the one". If the feeling is not mutual the relationship is destined to fail. As difficult as it may be for you to imagine right now you would be better off moving on. With 7 billion people walking the planet the odds are in your favor there is another girl who would love to have a man like you in her life even if she could only see him every other week. Best of luck!