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http://www.uesp.net/wiki/Morrowind:Ahnassi,_a_Special_Friend
The currently broken quest stage is the one where you have to cure her mate in St. Olms' canton from skooma addiction. If you do it, and return to her, she will not acknowledge your success, stalling the quest. The reason is clear in attachments - both her request and her thanks have the same quest stage number in condition (45).
The correct "I cured Ahnassi's mate" quest stage is not 45, but 75. Changing the value of her gratitude phrase to 75 makes her properly acknowledge your good deed, although she will still talk about her mate like he isn't cured after you ask her the "Share a care" topic later, since the >=45 condition on her request is too broad. It probably needs to be >=45, and <75.

I've noticed this too and
I've noticed this too and fixed it along with some other things. The quest doesn't work as intended altogether, even less so later on. Here's the isolated Ahnassi fix.
Edit:Added something I removed accidentally.