When you are accessing Project Web access using your browser, you might see the following message.
“Project Center cannot access the project(s) you are trying to view. It is most likely that you either don’t have permissions to view the project, another user has deleted this project(s) before you were able to view it or that another user is in the process of publishing the project.”
It is more likely to happen when you are accessing ‘Project center’ or ‘Resource center’. The only way I’ve found of removing this message is by disabling the IIS compression for .ASPX and .ASMX files from within the IIS manager.
If this didnt fix the problem, You might want to try updating the index statistics for the Published project database via the sp_updatestats stored procedure.
You can also try increasing the Application Pool Performance idle timeout. Since the PWA access the database to list all the projects, it might time out sometimes.