Completed tasks are dropped out of projects after a few days?
Can I adjust a setting so my completed tasks do not drop out of my active projects?
Your completed tasks are never removed from your projects, they're stored there forever unless you click on the "Delete completed" link in the bottom-right corner of a task list.
Please note that if there are a lot of completed tasks in a project, you have to click "Get more" to view them all.
Alternatively, you can view all your completed tasks in the "# Completed" list in the top-right corner - this list won't be deleted even if you delete the completed tasks within the project.