Yes. VoiceZone® Connect will display the 50 most recent voicemail messages. If you do not delete a message, it will remain on the application as long as you do not exceed the 50 message limit.
If you wish to store the message on your computer, you can log onto VoiceZone® and download any of your stored voicemails to your PC/Mac. Voicemail messages are automatically saved on the Time Warner Cable Voicemail system until deleted.