。
Why is she keeping so quiet?
Literal
She [topic-は] why so silent-is [explanatory-の] is [question-か]?
あんなに ('to that extent, so much, like that') is the so-series demonstrative degree adverb — referring to a level of something the listener is presumed to know or has been observing. 黙る ('to be silent, fall silent') paired with ~ている gives 'is in the state of being silent / has been keeping quiet,' the resulting state rather than the moment of becoming silent. Together with なぜ and のですか, the sentence captures puzzled bafflement at her continued silence — a question seeking explanation rather than information.