Bingo! I am having this problem now and I just replaced my SIM card because the other one died. I though it was because I was using a Movistar SIM before.
The one that comes up when the phone is turned on is "New Voice Message" and the VM icon is the tape but it has a "blank" tape in there (if that makes sense). Usually when I have a new VM I will get the message "New voice message on Line 1" and the VM icon will have black dots in the cartridge.
So for some reason the phone is being notified in a different way every time I turn it on. If I get a VM and delete it, it gets the VM clear SMS and it stays that way until rebooted. The funny thing is, the message comes up as soon as the phone turns on, before it registers on the network.
I'm thinking it's an issue with the newer SIM cards. My previous SIM card was from when I originally signed up with T-Mobile 2 years ago.
edit: when I delete the new voice message from the mailbox, the phone receives the SMS that tells it to clear the icon, and the message "New Voice Message" pops up for a second, then it blinks and then it disappears along with the VM icon.