Putting "automated testing" into the last 1% is the issue right there. It needs to be part of what you are doing from the start. You are done when your automated tests are complete and reliably green, not when some underpaid tester in Bangladesh gives their thumbs up.
Ideally your documentation is tightly integrated with your tests too, then it will be done as well and won't go stale.
Ideally your documentation is tightly integrated with your tests too, then it will be done as well and won't go stale.