All voicemail notifications are delayed anywhere from 4 hours to 4 weeks. This problem has been happening for over 4 years.
Verizon blames Apple
Apple blames Verizon.
I think it is network issue on the backend of Verizon. I tried just about every method, including a factory fresh install of iOS. Have upgraded phones and the problem continues. I am on the legacy grandfather unlimited data plan as well.
Please see the attached screen shot. Time is 6:02pm voicemail is from 1:59 pm and it is just sending the notification. Also LTE or Wifi doesn't affect the problem.
Screen shot of the problem
link - "http://designpg.com/1.png"
I understand the importance of receiving your Voicemail in a timely manner, and we can certainly look to see what is going on. As voicemails transfer via a cellular data signal, do you ever turn off your cell phone data on your phone? *Gert