MCPOPP... since I am having the same issues, my problem isn't resolved... so I added onto this posting.
AliciaS_VZW, To answer your questions...
Additional triage information:
So for sure, if I disable the Wifi setting, I can update the Visual Voice mail now. However, before a month ago, I never had to do that... as I only had to ensure Data was on.
After suffering the problem with Premium Visual Voice mail failing to send even a notice of messages, spending more than 2 hours with VZW techs, and running through all steps listed below in answer #17, I checked the status of "restrict background data" for voice mail. It was set ON. After unchecking it, and for good measure and prudence clearing data from the voicemail app, things have gotten back to normal. I did not have turn off wifi, and did not drop down to basic. After clearing tbe voicemail data, I rebooted the phone, tapped the voicemail icon, went through welcome/initiation stuff and made a test call to the mobile from an other device. Within one minute the phone indicated new message received, coumter on the voicemail icon lit up, message sitting in the new messages window.
Apparently, restricting backgroind data for voicemail (as a battery conservation method) caused my problem.
On my Samsung Galaxy S5 with Marshmallow and VZW VM v 4.1.15 this is how I turned restriction off:
Settings | tap Data usage | scroll down to Voicemail | Tap | scroll down to Restrict background data and uncheck it.
To clear VM data:
Settings | tap Applications | scroll down to Voicemail |tap | tap clear data. This will
essentially reset VM on your device (not the switch) | tap Voicemail on the home screen/desk top | go through the initiation dialog | run a call- in test.
It worked me... so far!