Why can I not place a pregnant woman to work but others work while pregnant?

Well I would first suggest to close the game, remove it from background and lock your phone to start the garbage collection. After that reopen the game and try again.

If this doesn't work, try to move her to another room. Maybe there is just a bug with that room.

I've read the suggestions here and agree with them, but just in case you don't want to leave the game to come back to it, you can send in enough people to push the pregnant woman out of the living quarters. They only get stuck in that particular room.

As others have said, it's a bug, and it still affects the game, at least the latest Android version.

Along the same lines as NTN's answer, during an invasion or infestation, the stuck pregnant woman will be forced out of the living quarters when the pests invade her room. You'll be able to assign her to any other room after that.

It's nothing you can force (or want) to happen, but if you have a stubborn pregnant lady in the quarters and you happen to be "awarded" with an invasion, you'll know that at least this problem will be fixed. She will be either forced out of the room or, if she dies, well, that fixes the problem, too.