Having the same problem and it just noticed that it started over the weekend, I have an HTC Windows Phone 8X running 8.1 via the “Preview for Developers” app, and whenever accessing Cortana using voice commands either from Bluetooth, or built-in microphone she responds “Sorry, I didn’t get that”. I know that the microphone works because using email I could dictate my email word for word, but Cortana isn't listening, or can't hear me.
I know that the Cortana that I have is still under Beta, because HTC/Verizon hasn’t (and I’m guessing they have no plans to do so in the foreseeable future) released and authorize update for the HTC Windows Phone 8X, so I’m stuck in Beta until I’m eligible for a new phone later this year.
If anyone finds out how to get Cortana to hear me again please post the fix.