I experienced loss of important archived voicemails on my Iphone after restoring my Iphone 4s to Iphone 5 using ITunes backup files and again about 6 mos later after restoring another new Iphone 5 with a recent ITunes backup after water damage occurred to my first Iphone 5. Nobody in my local Apple store or on Apple phone support, including a "senior technician" had any useful knowledge to assist me with this issue. Ultimately, I spent many hours researching this myself and found that Iphone voicemails are available for a limited period 30-90 days depending on the carrier but more importantly, voicemails ARE also indeed archived on an ITune backup. These voicemails are archived regardless of age assuming you didn't delete them off your IPhone before last backing up your device.
So, if you lost or damaged your iphone but have an ITunes backup, all you need is an ITunes extractor, unfortunately not available through Apple. There are several ITunes extractors available for music, photos, SMS files but most do not read voicemails. I successfully extracted from my ITune backup file all my voicemails, old and current using http://www.backuptrans.com/itunes-backup-extractor.html (Windows and MAC versions available). A life-saver!