It is difficult to provide you a logical solution with only the sketchy problem descritption you provided. If you provide a more detailed description of your site/OU hierarchy and your current implementation, then we may be able to give you better answers.
How have you configured your users to execute the logon script?
Do you want all users to execute some script?
In what specfic cases do you not want the script to execute?
What is wrong with the script starting to execute and then terminating?
