I’ll flesh out my comment into an answer. I have a few suggestions for why they might keep her in Malfoy Manor, not Azkaban:
- She has valuable information about Dumbledore’s Army (the DA).
Luna is one of the leaders of the DA, and I’m sure the Carrows know it. I bet the other Death Eaters do as well – remember, the DA is one of the few pockets of organised resistance, and would be on the radar of the Death Eaters. (Or, more likely, something they tease the Carrows about whenever they leave Hogwarts.)
The Carrows already have Luna trapped at Hogwarts, so they wouldn’t go after her just for this reason. But if the other Death Eaters happened to pick her up? They might bring her in for questioning – she’s more useful than your average witness.
- She’s a known troublemaker.
As leader of the DA, she’s been stirring up trouble for the Carrows at Hogwarts. And as Neville explains, the DA have been doing so without the Carrows knowing how they communicate. That must be infuriating.
If I were the Death Eaters, I’d want to isolate her from anybody whosewho is anti-Voldemort, especially in Azkaban. You don’t want to run the risk of her stirring up more rebellion.
- They can keep Xeno in the dark about what’s happened to her.
Xeno will stay in line for as long as he thinks Luna might escape unscathed. When the trio meets him, he doesn’t know if she’s dead, imprisoned, or something else. By keeping her completely isolated, they can stop anybody finding out what’s happened to her.
By contrast, if they sent her to Azkaban, word might get around the prisoners that she was still alive. Even if they keep Xeno away from her, it’s still conceivable that he’d find out she’s alive. Better to keep her totally isolated.
- Some of the Death Eaters have a personal score to settle.
Remember that two years ago, Luna fought toe-to-toe with Death Eaters in the Department of Mysteries. She was just fifteen. I’m sure some of the Death Eaters remember her, and would appreciate the chance to let her know how they feel.
Does that need you to keep her at Malfoy Manor? Probably not, but it might get her picked out from a group of prisoners going to Azkaban.