I have read thru all the forums about this same issue and nothing has helped me. Called customer service twice and no help. I've reset network settings, turned off wifi, etc.
Sometimes I don't get any VM and all of a sudden I get like 5 from a month ago. If I call my voicemail, I can see if I have new VM and listen to them there, and then right after, the vm's will show up on my iphone 6+ so I can listen to and delete from my visual voicemail. But I have to keep calling my VM just to see if I have any new VM or not.