First of all what is the Status Result and Return code of your scheduled task?
If you right click on the scheduled task, click info and get the number in the ID box. Look in you cores LDLOG folder find the scheduled task log with the ID number in it and see what it says.
Also I noticed the emergency distribution uses multicast, do you have multicast Domain representatives setup in each of your subnets?
I called Landesk Support and had my issue resolved. ultimately I had to restart the service on the core server.