Actually, the same thing happened Thursday night/Friday morning, but with much less dire consequences. I didn't hear the phone ring, in a noisy room, and didn't get two voice mails till Friday morning. Fortunately, my manager called a third time, and I was in a nice quiet place to hear the phone ring Friday morning.
I rebooted several times (we aren't allowed to have our phones on at work) since Wednesday night, and I noticed Sunday morning a "prompt" for my voice-mail password. My brand new iPhone 5 had been bothering me with "prompts" for an old Yahoo e-mail account password, so maybe I just didn't notice one for the voice-mail password. But I did get the voice-mails prior to that-- just 14-16 hours too late.
I really hope I don't lose my job over this software issue.