How Do I Fix Visual Voicemail When It Says It's Currently Unavailable?

The first thing to try is toggling Airport Mode in hopes that this forces your cellular provider to regain its signal. Go to the Settings app, switch Airplane Mode to off, then switch it back on 30 seconds later. If that doesn't work, go to Settings > General > Reset and select Reset Network Settings. You also might want to try powering down your iPhone and turning it back on. Worst case if it's still not working you can tap the "Call Voicemail" button below the error message and listen to your voicemails the old fashioned way.