So many times I have heard this and perhaps have been guilty of saying it too - why don't you speak up? Why don't you say something? Why don't you share?
And the other person clams up some more.
When a person does not speak or open up or share, it could be because they do not feel safe enough to speak up and be themselves, to share what they think you might reject. They are unsure of your responses and then on top of it they have to hear you push them into - share, share, share.
Why? So you can say something unpleasant about it?
Most cases I think that's the issue. One way is to make it safe enough to share.
If this does not work, then probably you are talking stuff the other person does not want to talk about. She is bored or not interested. Change the topic and talk of something they might be interested in.
Do it with love and compassion. Not as a job ticked so you can later say 'I tried my best but she would not speak.'