No, she shouldn't be cured. That's ridiculous.
The way Winick does it is just fine; bring it up once in a while to remind people, but not overwhelm the story with it.
And I think you're far, far, far understating the "only three times" that it's been brought up. The first time, in Green Arrow, there was an entire storyarc dedicated to it. It's practically ingrained as her origin as Speedy.
The second time, in Teen Titans, it was part of an intrinsic subplot about the secrets that the Titans keep from each other, and how they needed to be able to trust each other with these secrets or risk tearing each other down like the Justice League. Letting her friends know about her disease was a huge step for Mia, and a turning point for the rest of the Titans too.
The third time, on the island, Mia and Connor had a lengthy conversation about how it was progressing, and Mia expressed concern that she was experiencing a bunch of side effects from the drugs that she's taking.
I don't know about you, but those seem like pretty significant touch-on points to me. What more, exactly, do you need? For her to be obsessing about it every single issue?