Hi Dav, welcome to the forum!
I'm not entirely sure what is causing your problem and it's not one I've heard of before. Aircraft are either transmitting position information, or they are not - so you should get consistant positions on the map.
When you say your antenna is in sight of the aircraft, where exactly have you got your antenna?
Also, might there be interference that could be affecting your reception?
You say that you can plot a departing aircraft until 3000 ft, does it ever appear again on the map as it climbs? Can you see other aircraft all the way through the climbout?
Also, you say you are not getting the aircraft on the map until it is turning and going into land, what range and altitude is this?
Maybe a screenshot might help to understand your problem?
All the best
Allocator