Any message that is saved on your phone will remain so long as space is available. Voicemail messages that reside on servers are deleted by the carrier. Read messages are deleted after five days, and unread messages are deleted after 20 days. Once a voicemail message is deleted, there is no way to recover it.
You may also archive messages by forwarding them to an email address. There is an Auto-Forward to Email feature for premium Voicemail-to-Text subscribers that automatically forwards messages to a designated email address.
For further Visual Voicemail support, go to the customer care page on your service provider's web site.