Firstly are all zones closed when you are arming the system and are you exiting by the correct entry/exit route?,
If not user error like most on here it could be a E/E fault so check the door contacts or better still do a walktest to see if all sensors on the system are working correctly.
Suppose it has'nt been serviced for a while and now could be a good time for considering an upgrade to a better panel.
e manno
February 2013