Team System Reporting features uses SQL Server Analysis Services at its backend; it creates and maintains an Analysis Services database with name, TfsWarehouse. From few days, our reports were not working; today I invested some time in learning how the things work to troubleshoot the actual problem.
I found out that the TfsWarehouse database got corrupted (for some unknown reason), I found the setupwarehouse.exe tool and warehouseschema.xml file in the TFS tools folder with which we can re-create the warehouse database from scratch. I simply stopped the Analysis Service, deleted the database files, restarted the service, and then delete the database using SQL Management Studio (earlier it was not letting me do this) and then using setupwarehouse.exe and warehouseschema.xml from %ProgramFiles%\Microsoft Visual Studio 2005 Team Foundation Server\Tools, I recreated the database. After processing the Team System cube the Team Project Reports started working!