Hi Jan,
You should probably change the association from ‘db objects*->* exportdoc’ to ‘exportdoc*->*dbobjects’.
This way your dbobjects will not be changed, only your exportdoc.
So for everyone: Sjors answer is working fine!
Just change the association in the domain model to many-to-many and then set/initiate the association (during the iteration) from the export object instead of from the object itself.
If you have set the "deleteAfterDownload" to true for your export object there also shouldn't be any problem from a data perspective.