Hi I'm having the same problem. Just started last week and also won't let me leave a voicemail to that same contact. The voicemail message stopped after I said about 5 words and said something along the lines of "Voicemail not recorded due to no message heard" as if I hadn't been talking. I haven't tried a voicemail since last week, so I'm not sure if that issue is still happening, as well.
I would be concerned too if I were having any trouble sending messages or leaving voicemail messages. Do you have any trouble in sending text's or leaving voicemails to any other number? Can you please test?