I just wanna say thank you for your wonderful suggestion! I, too, lost my father and I had accidentally also lost his voicemails on my phone recently. I was crying and panicking because I thought that I won't ever be able to get back those precious voicemails, but then I found this forum, and only your suggestion proved to be successful! I'm so grateful! And of course relieved that I was able to get back what I once thought was impossible, plus more! I now have so many voicemails from my father, most of which I forgot that I had in the first place! I even have access to tons of other messages from various people over the years that I'll leisurely look through at a later time.
So thanks again!! Perhaps one might say that I'm being emotional over something a tad trivial, and while I agree that getting back voicemails is certainly not as good as getting back my father, I'd rather have his voice and memories with me than nothing at all.
P.S. To everyone who needs to recover old voicemail messages that can no longer be found in your phone, please get iExplorer from Macproplant...it really works!
http://www.macroplant.com/