Can a man and a woman that talk (albeit via text) daily be strictly friends?

We started talking about 3 months ago and have met with friends a few times and alone (over coffee) only once. It's been a while since I've actually seen her due to various cirstances (I was carless for about 2 months and she leads a busy life) but we talk EVERY SINGLE DAY.I talk to this girl more than I talk to my best friends. To be honest its very frustrating. She always balks at the idea of meeting with me but when I don't text her she asks why I'm so quiet. I realize that this is a ridiculous problem bordering on the adolescent but any outside appraisals could only help me.