Why is the IFE only available after take-off and shut off before landing?
They do this for the same reason they make you put away all electronic devices during that period of flight. The first minutes of a flight (take off and climb out) as well as the last few (approach and landing) are the most critical and statistically the time that if things are going wrong they will go wrong. As such airlines shut down the IFE systems and ask users to shut down personal devices so that they can hear, and more importantly respond to any emergency directions that may be given during this critical time. 



2019 Update: Since this original answer was posted some airlines now allow the use of "small personal electronic devices" in all phases of flight.