If she says yes, ask her to suggest a date that works for her. And I agree that using nonanswers to let people down is annoying, especially that particular one.
At least ones like "I'm busy" don't say the exact opposite of what they literally mean.
Basically, she's giving herself the option to say yes (or no) if you decide to ask again. Whenever I've gotten a real raincheck, like from a store, it's been up to me to come back to the store and say "Oh hai, I got this raincheck that I'd like to use, please." I don't see why this metaphorical raincheck needs any different protocol.
The term has been extended by merchants whose supply of a particular item has run out, to allow a customer to purchase the same item in the future, at the same price as the currently unavailable item.
She said she'd take a raincheck, as she already had plans for that evening.
I don't think it would hurt to try again, but this time instead of asking a specific date, just ask if she'd like to go to dinner sometime.
Then she can either say yes or no and an honest woman should say no if she's really not interested.
Doesn't that imply that she is the one with the raincheck, and gets to go back to the store? In the vast dating experience of the Teeming Millions, does this usually mean "I am tactfully telling you no" or "I'd sure like it if you asked me again." I realize that it could mean either, but I'm betting it means the former about 90% of the time.