I recently had a problem where suddenly TFS stopped sending emails and alerts. Furthermore, there was a permission bug with all new projects: The permissions were working perfectly in the SharePoint Site, however no one had the permissions in TFS Web Access.
The problem was that the Visual Studio Team Foundation Background Job Agent service was stopped. The Visual Studio Team Foundation Background Job Agent service provides a general scheduling mechanism for Web services and jobs for Team Foundation. This Windows service is also used to run the tasks spawned by various wizards, such as the New Team Project wizard and create a Team Project Collection wizard. The service uses the service account for Team Foundation Server (TFS), referred to as TFSService. The service runs on any server that is running a Web service or Web application in the logical application tier for Team Foundation. To operate correctly, the service account for the Team Foundation Background Job Agent service must have the permissions required for the tasks that it performs.
The service should be on Automatic Startup and should always be running! If you ever experience problems like the ones I had, make sure the service is running!