iOS has configurable content restrictions that can potentially prevent the Duo Prompt from displaying correctly.   If a user sees a grey box or white screen instead of the Duo Prompt on their iPhone or iPad, check if content restrictions are enabled.

 

Some Parental Control apps can also prevent the Duo prompt from displaying correctly.  Some of these apps use a VPN connection, and that connection can keep the device from connecting to the internet properly.   Verizon Smart Family app and OurPact have been known to cause these issues.  Once these apps are removed, Duo will function properly.
 

For iOS 12 and Above:

Content and Privacy Restrictions can be completely turned off.  To find this option go to Settings > Screen Time > Content & Privacy Restrictions and toggle to turn restrictions off.

 For older iOS versions:

For older iOS versions, you may have to use the following navigation:

Navigate to Settings > Screen Time > Content & Privacy Restrictions > Content Restrictions > Web Content.
To altogether disable content restrictions, uncheck Limit Adult Websites.
If you do not want to disable content restrictions fully, you can add duosecurity.com to the whitelist within the Content Restrictions page on the iOS device.  This will allow the Duo Prompt to display even if content restrictions are enabled. Note that if you are opening Screen Time for the first time and haven't set up the feature, you will be prompted to set up the phone either for yourself or a child and will have the option to set a passcode.

Some older iOS versions may also be found by navigating to Settings > General > Restrictions > Websites.

To altogether disable content restrictions, uncheck Limit Adult Content.
If you do not want to disable content restrictions fully, you can add duosecurity.com to the whitelist within the Content Restrictions page on the iOS device.  This will allow the Duo Prompt to display even if content restrictions are enabled.