How long are completed tasks kept?
Completed tasks are stored forever. If a completed tasks is moved to the history, you can click on the "Get completed tasks" link at the bottom and it will stay there forever, but please note that it may be required to click on this link multiple times as not all tasks are loaded at once.
These tasks can be removed from the project at once by clicking the "Delete completed" link.
The other option is the "View completed" list - it's available when you either click on your Karma in the top-right corner or hover over it and choose "View completed". This is a complete history of all task completion events and here you can remove each event separately, but clicking on the "Delete completed" link within a project won't affect this list.