I feel for you OP, especially as I fear I will be in your situation in about 7 years' time when Ds2 hits a similar age!
But I "deserve" it, as I was also like your DD.
Even now I still can't really identify what the issue was - I was very bright, and before I got to senior school, hadn't really had to work hard at much to get good results. My junior school didn't go much on homework, just weekly maths and the occasional project, which I think caused a problem because I just didn't have a "home work ethic" at all so it came as a bloody great shock to me to have homework for 3 subjects a night sometimes!
I also have this weird thing that means I can't just hand in a badly done piece of work - I have to do my best on it, but if that's difficult, then I'd rather not do it at all than hand it in done poorly or only half finished, if you see what I'm saying. It's REALLY stupid, but some kind of perverse perfectionist thing going on, apparently.
Also I'm Procrastinator General. Even if I start something well ahead of time, I'll do so much and then stop, and think "I've got ages to finish that" and then it'll be the night before and a 2am finish to get it done in time (SO MANY FUCKING TIMES!!)
I have no idea, literally none, as to what could have motivated me to do it differently. I did school, A levels, university, a Masters degree, and then a diploma in a completely different area to change careers (the latter 2 of which I funded myself) and STILL my "work ethic" just didn't change. I'm not proud of this, far from it! Annoyed by it though - just disorganised, timewise, and lazy I guess.
I wasn't like this at work!
In terms of your DD the only thing that may help, if you haven't already tried it, is to see if anything else is going on - if she's had a drop in motivation, is there bullying? is she bored? has she been picked on for being a swot? or does she just find it all totally pointless?
And then the ultimate - which I would have hated but it might have worked, I don't know - is to take away her reading books and leave her only with text books and school work to read. I used reading (I read A LOT) as escapism - I wasn't particularly unhappy, but I wasn't thrilled with life either, didn't get on with my siblings, didn't have many close friends, had some low grade bullying most of early school - reading was so important to me. I'd have been very upset to have been removed from my books.