Why don't incomplete surveys transfer into SharePoint, even after 1 week?

Are you using a workflow? I don't believe workflows trigger when an in-progress response is closed due to inactivity.

The workflow "Survey Response" is only triggered when the respondent "submits" the survey (responds to the last question). Unfinished surveys, and surveys marked closed (either by the response setting or manually closing), to not trigger the "Survey Response" workflow.
However, there is a solution to get the "Survey Response" workflow to trigger for all surveys.
Add the following condition to the workflow:
Any of the following are true
Embedded Data Finished = 0
Embedded Data Finished = 1
You must enter the word Finished as it will not be in the dropdown.
With this condition, the "Survey Response" workflow will trigger for ALL surveys.