Once you start watching a film, you'll have 48 or 72 hours (depending on the title) to watch it without using another play credit.
In-progress films appear on your Continue Watching list, which is accessible from the Continue Watching shelf on the Kanopy homepage and from the My Lists page.
At the top-right of each film on your Continue Watching list, you'll see the number of hours remaining until your play credit expires.
If you hover over a film on your Continue Watching list, its title card will also display how many hours you have left until the play credit expires.