Not the error message that you get. Open up the SQL Server error log and see if there are any errors in there that may suggest why the trigger failed. If not, change your trigger as follows and then see what's in the error log after another login attempt

CREATE TRIGGER [LoginAudit] ON ALL SERVER

WITH EXECUTE AS 'sa'

FOR LOGON

AS

BEGIN

BEGIN TRY

INSERT INTO Audit_Log

SELECT @@SPID ,

SYSTEM_USER ,

HOST_NAME() ,

HOST_ID() ,

CURRENT_TIMESTAMP ,

APP_NAME() ,

DB_NAME()

END TRY

BEGIN CATCH

PRINT CAST(ERROR_NUMBER() AS VARCHAR(5)) + ' ' + ERROR_MESSAGE();

END CATCH

END

GO