I live in a basement apartment where I cannot get cell service. I am using wi-fi calling on an iPhone 5s. This works perfectly for making and receiving phone calls, but I have noticed that I never receive notifications when I have a new voicemail. I only see that I have a new message when I am physically in an area where I get cell service.
Are you running the most up to date version of iOS for your phone? This issue is due to the specifications in the carrier-settings update included in iOS9 starting on September 25th, 2015. As far as I'm aware, it was resolved in an iOS update since then.