Apple has updated its iPhone X repair policy for a limited number iPhone X devices with Face ID problems. Apple Stores and Apple Authorized Service Providers are authorized to replace your entire phone, instead of just the display (via MacRumors).
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iPhone X Repair Policy
First, Apple Stores and Apple Authorized Service Providers have been told to run diagnostics on the iPhone X’s back camera. If a repair to the camera doesn’t fix any certain issues with Face ID, then the whole phone will be replaced.
In order to provide the best customer experience, if a customer reports that their iPhone X is having Face ID issues, you may be able to resolve the issue with a rear camera repair. Run AST 2 on the customer’s device to check the camera. If the diagnostics find issue with the camera, perform the repair to see if the issue is resolved. If the issue is not resolved, perform a whole unit replacement instead of a same-unit display repair.
It sounds like there might be a connection between the iPhone X back camera failure and the front TrueDepth sensor system. You can get an appointment through the Contact Apple Support page.
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Is there something more specific than “Face ID issues”? I have occasional problems with Face ID; how do I know if that qualifies?