What does "Keep the lender's access open" do?

It stops the lender's access ending while you still owe it reports. Access shared with a lender ends after 90 days, but reports go on for the life of the loan, and a report added after someone's access has ended never reaches them. So when you set up reporting, the box that keeps that lender's access open is ticked, and the end dates of its people go, unless one has already passed.

You can set a date again on each person's Manage access page. While you report to a lender, its page warns you about anyone whose access ends within 60 days, or has ended.