See if the following troubleshooting steps can resolve this issue:
1. Ensure the Lightning to HDMI adapter is securely connected to both the iPad Air and the HDMI cable. Sometimes a loose connection can cause problems.
2. Try using a different HDMI cable to connect the adapter to the projector. The cable may be faulty or incompatible with the projector.
3. Update your iPad Air to the latest version of iPadOS. Software updates often include bug fixes and improvements that can address compatibility issues.
4. Reset the settings on your iPad Air. Go to "Settings" > "General" > "Reset" > "Reset All Settings." Note that this will not delete any data but will reset all settings to their default values.
5. Restart both your iPad Air and the Epson Pro projector. Sometimes a simple restart can resolve connectivity issues.
6. Check if there are any firmware updates available for your Epson Pro projector. Updating the projector's firmware may improve its compatibility with the Lightning to HDMI adapter.
7. If possible, try connecting another device (such as a different iPad or a different brand of smartphone) to the Epson Pro projector using the same adapter and cable. This will help determine if the issue is specific to your iPad Air or the adapter itself.
8. Since you already contacted Apple Support, consider getting back to them and provide them with the details of your troubleshooting steps. They may be able to offer further assistance or suggest any known issues with your specific setup.
If none of these steps resolve the issue, it's possible that there may be a compatibility problem between the Lightning to HDMI adapter and the Epson Pro projector. In that case, you may need to consider alternative ways to connect your iPad Air to the projector, such as using wireless screen mirroring options or exploring other adapter solutions.