] She felt assured of the Captains affections so she decided to write him; the "challenge" thus being over for Tilney, he moved on to Charlotte Davis.

That might be. OTOH, it might be that after she wrote him, Frederick realized she was a lot more serious than he was, and it scared him off. (Like the joke about the dog who chased a car but didn't know what to do when he finally caught it.) If he had continued the relationship he might find himself forced to marry IT, rather than just have a bit of fun.