Hi there, Skylineprints. Thanks for getting in touch with us on Apple Support Communities!
It sounds like you're having trouble connecting with FaceTime. We can help.
First, let's see if we can determine if this is an issue with a specific contact, or with all contacts in general. Are you able to FaceTime other people without issue, or is the same thing happening?
If the FaceTime calls go through with other contacts, you may want to check your Do Not Disturb settings. In iOS 15, you can find these by tapping Settings > Focus > Do Not Disturb to make sure you don't have any general restrictions. If any are on, let's turn them off for now and test again. Another thing to check is if your contact has the issue with anyone other than you as well. This will help us determine if it might be a setting on their end that is causing the behavior.
If the same thing happens with other contacts, and you've already followed the troubleshooting steps you mentioned in your post, you might want to Contact Apple for support and service.
Hope that helps!