I have a Surface Pro setup in my kitchen for my family to use. I have Cortana set up on it. I've had this set up for several years. We have this issue where sometimes Cortana won't respond on the first attempt. I say "Hey Cortana", I hear the chime and see her window pop up indicating that she's listening...I ask my question. Sometimes I see the question text forming in the box, sometimes not. She then stalls out and disappears. I have to say "Hey Cortana" a second time and then she works correctly and responds.
This happens daily, usually after she hasn't been asked a question for a long duration of time, like overnight. So, we typically have this experience on the first question we ask in the morning. But, I've also had it happen later in the day, if she hasn't been asked a something all day.
This has been happening for years. I've resetup Cortana multiple times and even reinstalled the entire OS and it still happens. So, it seems that this is a bug.