I had a child in my class who was an elective mute. Within the first few minutes of meeting her it became apparent that her parents anxiety led them to prompt her almost constantly "Say yes to the teacher" or to bombard her with questions trying to illicit a response "This is a nice classroom isn't it?"
It was a nursery class and many of the children were happy to play alongside her without talking to her directly, just talking to themselves as young children do. Within a week she was talking to the other children. They demanded nothing from her so she could converse on her own terms.
As adults we adopted the same approach and it took a couple more weeks before she spoke to us. We never prompted her to speak and the questions or comments we made had a real purpose, they weren't attempts to get her to say something.
Can I ask if the family, without even realising it, are prompting and pushing. Children can be resistant or she may have sussed out that it's a good way to get extra adult attention!