Automatically log SQL query, if it throws some exception in SQL Server 2005

I have a huge WinForms application having SQL Server 2005 as database server. The application deals in financial stock markets, and during market hours, SQL requests can range from 2500-3000 per minute approximately. Many times on production we face an issue when SQL query fails, and we get errors. It becomes really difficult of reproduce that issue for debugging purposes. Is it possible to automatically log that particular SQL query which failed to execute successfully. Logging each query would be costly, therefore, only if it fails, then only it should be logged.