Roverlike

What you explained is expected passive immobilisation of the car. Since there is no delay when opening and closing the door by the key, delay you can see on pscan can be related to the software and hardware recognition time.
In these circumstances there is nothing I can put finger and say this might be the problem, except you cannot get EKA to work.
If you tried and set EKA to lower values and no luck there, I am out of ideas as well.
In this case car behaves like chinese version of the car (versions later then 2005) in which seems like EKA code entering feature is disabled at all.