I had this problem with T-Mobile's Visual Voice-mail app.
What I found was that when I connected to my T-Mobile voice-mail directly through the notification pull down shade, that after I listened to the messages & disconnected the call, the notification remained. It wouldn't clear even after a reboot. Eventually, I realized that if I opened up T-Mobile voice-mail app & connected through the app, the notification would clear. I spent weeks force stopping the app & clearing the cache before I stumbled upon the solution. I don't pay for their transcription service so I have to call in. (I use the default Samsung phone app.)
I don't know if this fits your situation, but that's how I eliminated the persistent voice-mail notification problem. I check all my voice-mails directly through T-Mobile's app & never through the notification shade.