Alarm trips when entry sensor is closed in Home mode

From what I understand, you should be able to arm the system in Home (and maybe even Away) mode with an entry sensor open (e.g. window), close that entry sensor at a later time, and the system will then monitor that entry sensor for future opening events.  This works if the system is armed and the entry is closed within a few minutes of one another.  However, I have found that when the system has been armed with a window entry sensor open, and then I close that window a couple of hours later, the system will trip and start counting down to an alarm.

Any thoughts or is the system supposed to behave in this way?