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You may need to describe the options you have specified for your container field in more detail. Ordinarily, duplicating the record duplicates all data in your fields--including a container field unless some other details such as an auto-enter setting or a script trigger performed script (with the trigger performed by the duplicate action) are clearing the field.
Also, could the container field actually be in a related record and not in the record that you duplicated?
I have a script example in here somewhere where you duplicate a parent record and all of its portal records that would server for that purpose.