Setting the objects to nothing won't change anything becasue VBScript's garbage collector already takes care of that efficiently. However, if you are using ActiveX Objects (through the CreateObject()) method, then some of those objects may not be thread-safe. That depends on the version of Windows you're running, which updates were installed, what drivers were updated, and so on.

For instance, there are several versions of the Microsost.XMLHTTP available, just like there are different versions of the DAO/ADO/OLEDB drivers. Those would be the prime suspects, along with application objects like Microsoft.Excel or Microsoft.Word.

If you are using an Access Database, the drivers used to access that DB are notoriously flaky in multi-threaded environments.

I am not pointing the finger at any particular object, just attempting to give you pointers to help you determine what could cause the issues you're running into.
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Technical Product Manager
I don't want to achieve immortality through my work; I want to achieve immortality through not dying - Woody Allen