You already answered your question, my man. You know you need to not do that. The big red danger light is flashing, and it's flashing for a reason.
Think on it. How many normal teenage girls, especialy attractive ones, constantly beg one guy for a meaningless one-night stand? Exactly. Girls like that can have sex any time they want with almost any guy they want, and they know it.
She is not looking for just one night of sex, no way no how. She's looking for something else, something she can hold over you for a long long time. It might be just sex to you, but for her it's a means to an end. If you bang her, it will (not could, will) come back and bite you hard.
Here's what you do: You keep refusing her, as politely as possible, and you do it IN WRITING. Text, email, whatever, just make sure your @ss is covered in writing. Cover yourself from every angle, multiple times and do it all in writing and keep those records.
Once you've covered your @ss as many times as possible with as much documentation as possible, only then can you bang her - on the verbal (no record, no witnesses) agreement that nobody will ever speak of it again in the future! Then if she texts you about the night you had together, you reply that you don't know what she's talking about. And if she tries to blackmail you, you've got loads of documentation showing that you refused her requests over and over, and not one record showing where you were willing to do it. Now your butt is protected, AND you got laid with a hot chick.
Two can play at that game, and turnabout is fair play.