Mark,
You can do that already, but you have to have the options set correctly.
Scroll down in the general options for these settings (copied from the docs page):
Show Expired Tasks? — If you want to save signup info even after the dates have expired, check this box. This ONLY affects the signup lists on the ADMIN side. The public sign up sheets will never show tasks/signups that have expired.
Automatically clear expired signups? — Enables the hourly CRON function that checks for and deletes expired signups from the database. If you want to save your signup data after a task date has passed be sure to uncheck this and then check the above option to be able to view the expired tasks/signups on the admin side. If later on you want to manually delete all your expired signups, use the button on the CRON Functions page. For example, it is useful to clear all signups so that you can alter the dates on a sheet and reuse it for the following school year.
You need to make sure the first one is checked and the second one is NOT checked. Checking the first option above will allow you to view expired sheets & signup info. However, if you had the second box checked, then you are out of luck as it will automatically purge signups from the database once the events have passed.