Easy2Sync for Outlook can not only start a synchronization manually, but also automatically, e.g. when you’re shutting down Windows. For this, you just have to mark the task for an automatic start or enable the automatic start for all tasks in the options. In the tasks you’ll find the right checkbox on the page "Automatic start" or in the Options on the page "Automatisation".
Please note that Easy2Sync must be running when shutting down. You can minimize the program into the System Tray (next to the clock). This can be enabled in the options on the page "Window".
Furthermore this function works only for a "real" shutdown, not for a Standby-Mode.