My software is up to date, and I can listen to my voicemail, but I still get the "Can't connect" message.
For me, I turn Wireless Data off most times as I like to save my data (not unlimited). I've noticed the same error when this condition is true. (I also had Wi-Fi calling disabled, FYI.)
Once I turn mobile data on, it works fine.
In experimenting, I turned Wi-Fi calling on and kept mobile data off. Rebooted my Pixel 2 XL and tried to listen to a voicemail, it sits at "Loading Voicemail" for a while and then says "Couldn't Load voicemail." As far as I can tell, it need mobile data turned on to use the "Visual Voicemail" features. If you have Data turned off, then you have to use the traditional phone method (non-visual).
FINALLY!!! Finally a simple answer to a simple problem that the Verizon employees seemed unable to address.
This is 2020, not 1990. I should not have to disable my wifi in order for feature on my phone to function.
We sincerely understand your concerns, Lemiarty. While technology has advanced tremendously over the past 30 years, your Voicemail box is still part our Verizon Wireless system. Are you able to access your Voicemail if you call *86 when you are connected to a WiFi network?