Ho trovato la risposta allo stesso problema in un post precedente.

Copia il combobox dal filmato, incollalo nella _rooot (quella che ti carica il filmato contenente la combobox), cancellala dallo stage in modo da lasciarla solo in libreria. Pubblica _root e filmato.


Dal sito Macromedia:

Issue
A ComboBox used in a SWF that is loaded into a level or target may not display or function properly (for example, labels may not display or data bindings may be lost).

Reason
This is caused by the v2 component architecture. This issue usually occurs when using v2 components inside a child SWF that is loaded by a parent SWF.

Solution
Add an instance of the component to the Library of the parent SWF (the movie that loads the SWF content):

Drag an instance of the required component to the stage of the parent SWF.
Delete the on-stage instance, but do not delete the library item.
Note: This will increase the size of the parent SWF and will force the client to download two copies of every component used. To reduce download time it is recommend that you used shared libraries in your final publication. For more information about using shared libraries, see Using Shared Libraries (TechNote 14767).