Well this is all still a fresh memory in my mind as I've spent the past six months off and on chasing around in circles with this issue on mine! I don't profess to have a microcosm of the knowledge or experience demonstrated here by other forum contributors but the recent slog I have endured upon new P38 ownership has certainly rounded off a few corners along the way and no doubt added a few more grey whiskers to my chin BUT praise be, thankfully I got the $πåߥ thing to work reliably in the end...
I have found that mine is very particular about how things need to be before it accepts the EKA too!! By this it needs to see every door, the hatch and the bonnet closed and fully locked first, a nice fully charged full battery and the driver's door handle needs to be fully closed flush with the door (mine can be allowed to stick 4-5mm out if it's not pressed home fully). I suppose also having it facing Solihull may humour it a bit too.
It would be highly likely that this has all been triggered after renewing the plip battery and your taking longer than a recommended time (a minute I believe). I have no idea how this should be so time critical and can only speculate that this is due to it retaining a memory of what is required from the last scrambled code it used whilst randomising the lock codes between the plip and the car which are now out of sync with one another and you now need to resync the key first. To do this turn the key to the lock position in the driver's door lock whilst depressing the plip lock button for 15 seconds or more then repeat with the unlock position and button pairing for the same duration. You then follow this by the EKA procedure.
Another thing too is the ignition key needs turning within 15 seconds of inputting the EKA and the door opened or it will lapse. There are x3 strikes for every attempted EKA but after x2, if you open and then close the driver's door this will clear and allow another x2 attempts which won't require the long winded 30 minutes cooling off of the key lock out.
In the end, the one main thing I was doing wrong with mine was assuming because there was no sign of a starter triggering the engine after trying an input of the EKA was to keep carrying on even where it didn't say the engine was disabled or key lock out until of course I tripped it into saying these. Ultimately it turned out that because a triggered starter is the actual confirmation of a correct EKA input that it was actually this that ended up being the culprit!! Yep, a sticking starter! If you switch the lights on and try the starter if they dim the starter is under load and drawing all the juice available from the battery. Try giving the fulcrum pivot point between the main starter body and the parallel solenoid a precise clout with a small ball-pein hammer!!
BTW, if this is something you don't usually have issues with, is it 100% absolutely certain that you're using the correct EKA and following the procedure as per the official handbook? I'm not suggesting you're not compos-mentis, just that you could be working on duff information from an incorrect reference point - my car's previous owner was mixed up with his 4 digits - they were the right numbers just in the wrong order! The local LR agent will still have this information on their database and by proving you're the genuine keeper confirming keeper and vehicle data this is available freely (in my local dealer's case anyhow!).
I completely expect my still green knowledge to be straightened out by those that have forgotten more about all this than I will probably ever know, but hey, every contribution stirrs the conversation which helps move things further along towards a resolution