iOS has configurable content restrictions that can potentially prevent the Duo Prompt from displaying correctly.
If your users see a gray box instead of the Duo Prompt on their iPhone or iPad, check whether they have content restrictions enabled.
For iOS 12:
Navigate to Settings > Screen Time > Content & Privacy Restrictions > Content Restrictions > Web Content.
To completely disable content restrictions, uncheck Limit Adult Websites.
If you do not want to fully disable content restrictions, you can add http://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: 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.
For iOS 11 or older:
This can be found on the device by going to Settings > General > Restrictions > Websites.
To completely disable content restrictions, uncheck Limit Adult Content.
If you do not want to fully disable content restrictions, you can add http://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.