Her default clothes are "hooded" and have no armour rating if you give her head gear with an armour rating she'll drop the hood and therefore the robes. She is probably treating the Archmage's robes the same way and the patch that fixed Morokei doesn't work for her.
Aranea is skilled in Light Armour, so you will get the best out of her if you use that anyway. I gave her all Elven gear with different schools of magic enchants - she's a good all rounder. I also gave he all the staves I could find and took her weapons off her.
Here's a video of her in action with my Dunmer Spellsword
http://www.youtube.com/watch?v=J3mwrQrBl7g