Why would she turn down a relationship?

Dude wtf. You're 26 and she's 20. That age gap is HUGE, in a developmental sense. It'd be a different story if each of you were 5 years older, 31 and 25, but she's pretty much new to adulthood, still figuring her sh*t out. Maybe she doesn't want to be held down by a guy, though her hormones/biology are prob saying different. Or she's playing hard to get, or she's just jaded, or... a million other things. I think you should back off and let her figure herself out!