When you password-protect a post in WordPress, a cookie is set to expire in 10 days which prevents the user from having to enter the password during that 10-day period. This plugin allows you to easily change the lifetime of that cookie.

0.2 - Added settings page; expiration time now based on a WordPress option.

0.1 - Defaults to 2 hours

Unzip into wp-content/plugins, then activate via the admin panel. Settings are in Settings -> Password-Protection Expiration.