Since version 0.6.0, you can set the 'Screensaver' in System Preferences and maintain the display content for a period of the day.

Open 'Preference' and select 'Disable "Screensaver" between' option and fill the fields of the desired period.

You must enable 'Screensaver' into your System Preference of course ;-)

You must restart SplitBrowser to enable this option.