There is a possible chance that your WiFi is the reason that you are unable to set up your greetings for voicemail. Many users solved their problem by changing their network from WiFi to Cellular data. Your carrier provides the cellular data and that can be a better choice for voicemail settings.
You can call your voicemail service to check your messages. Open the Phone app . At the bottom, tap Dialpad . Touch and hold 1.

Standard greeting with phone number: "At the tone, please record your message to [phone number]."
The prompt will stop appearing. If the 611 Automatic System does not work for your carrier, you can head to your carrier‚Äôs official website if youriPhone 6s keeps asking for voicemail password. From the myWireless Account home page, select Phone/Device then choose the Reset Voice Mail PIN link from the left column. Note: If there is more than one line on the account, make sure the correct wireless number is displayed in the Wireless Number list before selecting Reset Voice Mail PIN. To reset the password for any of the lines on the account, choose a wireless number from the dropdown menu and click Submit. In a while, iPhone will display "Password Incorrect - Enter Voicemail Password." Enter the last seven digits of the wireless phone number and tap OK. Log into My Verizon with your cell phone number and password. If you've set up a username, use the username instead of your phone number. Select My Verizon> Reset Voice Mail Password. Choose your cell phone number from the drop-down menu, and thenclick on "I Will Create My Own Password." Enter and confirm your new password. Click on "Submit" to save the change. Sign in to My Sprint with your username and password. Click“My preferences” tab. Under Things I can manage online, click on Change voicemail passcode. Enter your new passcode and confirm. Tap Save and you will get a message informing you the new password has been saved.