Well yeah, but with a person that gives a damn. Trust me, I more than anyone would fight to beat odds. But guess what? In a relationship, the other person has to want the same thing. If the other does, then it is literally impossible to have it fall apart at that point. However, if it's just you trying then guess what...
So relax, and keep looking. Because guess what, she doesn't sound like the person that gives a shit about you.