Can't get nine week old kitten to use the litter half the time.

She is nine weeks old, healthy (declared so by the vet) and has been in my care for three weeks. Week one, I bought kitten attract and had two different litters/boxes. Week two, I crated her and she went in the litter box. Week three, I let her out a few hours a day (had a litter box both in the crate and outside the crate, I showed her repeatedly were both were). When she's in the crate, she'll do fine. When I let her out, its like she forgets. Vet said not to worry?

Its my bedroom, so she is not roaming the whole house, and I've just added a third litter box. She was abandoned, so she had no one to teach her. 

You can try burying her poop or the paper towel soaked in her pee in the box. Does she share the box with another cat? She might be fussy about that. Good luck with this - it has to be the worst.

While I really really know this is frustrating, given the age at which you got her and the fact that she is only 9 weeks now, it is premature to panic/worry.  Sometimes the issue calms down once a cat is fixed (though I've found that more with neuters than spays).  Sometimes also they just have a eureka moment and that is that.  I would not seriously worry about this until she reaches at least 12 weeks and is also spayed.

That all said, what kind of litterboxes do you have? Are they uncovered? Are they different sizes (many cats like big boxes, so she might want a bigger one; some kittens are intimidated by a box that is too big so at this point she may want a smaller one too). Also pay attentiont o how high the sides are- does it seem a challenge for her to get in and out?  Do you have towels or a mat around the box for her (sometimes it is easier or even necessary to get them 'litterbox adjacent' first).

You seem vigilant about this but how often do you scoop? It is possible you are being too vigilant as well- as the comment above me said, some kittens (and even some cats) need a hint about where to go.  She may also want a different litter- I know cat attract tends to be recommended (and in these situations with my fosters it is what I use) but each kitty is different.

Is she confined to one room when she is out of the crate, or does she have full run of the house (or several rooms)? If the latter, she may indeed be confused about how to get back to the box.  She may also feel overwhelmed still when out of the crate and become slightly anxious which can make little kitten bladders harder to control.

If you ever catch her in the act, make sure you are picking her up and putting her in the litterbox.  If you ever catch her right after, same advice.  Make sure you are also putting her in there after each time she sleeps and eats (I know you said you've showed her many times but some kittens are slower about this than others). Do not discipline her in any way about this- it is certain not to improve the problem and may make it worse.

You don't mention if you've tried to show her how to use it? Have you dug around in the box a bit while she can see you with your fingers, or helped her dig a bit with her paws? Also, are you using a good enzyme cleaner to clean up after each accident?

I really do think that with some more time, patience, and persistence the issue will resolve.  As I said, I know it's frustrating but this is not unusual for a 9 month old, especially one in her circumstances. I am 99% confident that given 3 more weeks and (again, patience and persistence on your part) the issue will clear up.