When you unlock the car with the remote, it also disarms the immobiliser for a minute or two, then the immobiliser will turn on again unless the ignition key is inserted into the ignition switch and turned on, which should also disarm the immobiliser if it has come back on again, via the key reader. It sound like a problem the key reader, or the key itself. As well as the metal knob that contacts the key reader, theres also another small metal contact that touches the actual metal part of the igniton key, this is actually an earth to complete the key reader circuit, so the key can be read by the bcm.This can cause this problem if its not clean and properly touching the metal part of the key. To check it,just remove the two screws and remove the metal part of the key from the plastic fob,you should be able to see the small metal tab up inside the key locating hole in the fob.