More details needed. How did you offend her, how did you apologize, how did she respond to the apology, etc? It's especially important that you know for sure what it is that offended her, or you may have been apologizing for something that's beside the point.
I know don't get upset often with people to the point where I cut them off & won't accept an apology. I wouldn't say I'm easily offended either. However, if/when I do get upset, people often entirely miss the reason something actually upset me.
I'm wondering if, even though you apologized, you still display traits that raise red flags in her mind & indicate you're not worth the trouble. However, in such a position, I may hold someone at arm's length, but I probably will not make it obvious that I prefer to avoid them by giving them the silent treatment or anything childish like that.
Oh yeah....I'm guessing you want to re-establish communication? What's your motive for that?