There's nothing in built for that but you could set up CRON jobs on your server to do so, say deleting entries more than 7 days old. CRON jobs are outside the scope of this user-to-user forum, and you might have to ask your web host about such things.
I think it might be more difficult to do this than I thought, since each form's submissions are in a separate table, associated with that form, so you'd need CRON jobs for each form essentially. Not good if you have dozens of forms for different purposes.
I'm rambling, and don't know enough about that stuff to provide a real answer, sorry.