Thanks for reaching out in Apple Support Communities. I understand that you're having trouble playing Visual Voicemail messages and you're unable to play the outgoing message you have recorded. I know Visual Voicemail is an important feature to use and I'd like to help. I'd recommend following the steps below:
Set up Visual Voicemail on your iPhoneCheck your Visual Voicemail after each step:
Let me know what you find.
Best Regards.