The behaviour that is seen is that the project file is opened for a fraction of a second and closed, in the lower tab in the Project Pro client is displayed "closing project name" The issue cannot be reproduced but it could occur when a ressource is been taken out of a project and afterwards the save/publish job is failing for some reason in this way in the database a damage could occur resulting in a duplicate value.
The simple solution here is if you are still able to open the project plan from the PWA try adding a ressource via the Project Center to the affected Project that couldn't be opened in the Project Client. This solution is usually rewriting the duplicate value that remained in the damaged table.
If this doesn't solve your issue address the issue to microsoft support as some cleanup scripts may be necessary to cleanup the duplicate entries on the Project Server Databases.
Open, read, view ms project data via fix damaged ms project files