Is it possible to change the amount of time a user stays logged in for? Our users are getting logged out after 1 day.

Is there a setting that changes how long users’ sessions will last?
Yes! The setting is called userSessionDuration, and you can set it in your general.php config file, on a per-environment basis.

Here's an explanation of the values that you can use for the setting—for posterity: integers (in seconds), a PHP duration expression, an initialized DateInterval object, or 0 for "indefinite."

The link above points to the Craft 3 documentation, but the same setting is available in Craft 2.