I think I would have passed her while simultaneously moving to end the use of the testing. The more trained as sedai become where tel'aranrhiod (or however that's spelled) is concerned, the validity of the test diminishes. It's sort of like Ruidean (gosh I'm a terrible speller but on my phone so not spell checking! (Crazy face). Can it serve a purpose, totally. Is it reliable or necessary anymore? Perhaps not. I think the greater question is answering, what makes you aes sedai. Egwene already began changing that with ages and the kin shows power level doesn't always make right. So I would pass her, if nothing else, but to move on and show it's flawed. She failed but is clearly aes sedai, let's change what being an aes sedai means.
When I read the books, I didn't realize that it took around 20 years to raise an Aes Sedai. I think if I had spent ten years as a novice and then another ten years as an Accepted, I would not have been able to raise someone after such a short time without being angry Although, the times were desperate I guess, so maybe, maybe ...
I am biased and like Nynaeve and I know more about her than the Aes Sedai raising her, so I would have raised her, yes. BUT since they purposefully did everything to make her fail, I think they are biased too, which should not have been allowed! If they would have done everything to fail her, it is not a fair test, is it? I did like how she handled it afterwards though and she was way too advanced to not be allowed the Three Oats and the title of Aes Sedai. Many other Aes Sedai are acting even worse throughout the books, so...