。
She's worried she might end up turning down my request.
Literal
She [topic-は] my request [object-を] refuse [might it not be that-のではないか] [quotative-と] is-worrying.
The pattern ~のではないかと心配する is one of Japan's most common ways to express anxious speculation: literally 'worry as if [it isn't the case that X],' but functioning as 'worry that X might happen.' The のではないか frame turns a feared outcome into a tentative question, which the matrix verb 心配する then attaches to via the quotative と. With 彼女 as the topic of 心配している, the implicit subject of 断る is most naturally also her — she's anxious about the possibility of her own refusal, perhaps because she doesn't want to let the speaker down.