This one is puzzling to me. I'm not sure SL-00072 is going to fix the behavior.. but for $20, it's worth the shot.. plus it's a quick install too.
I'd be interested to know what the LED color is on the HIC module pre-start and post-shutdown.
I had some problems with the EMS Emergency switch early on.. it was my own doing though. As part of a bulletin to fix some solder joints on the main power board, I had to remove some components of the assembly..and I disconnected the wires to that switch. When I reassembled, I got confused as to which wires went to which terminal in the back of the switch (I took a photo, but it wasn't as clear as it should have been).. long story short, there was a short-circuit and the internals of the switch welded themselves into the ON position, despite the switch seeming to move normally. The 35A fuse popped, and kept popping until I fixed the wiring.. but the damage to the switch was already done..and it was stuck ON..
The real question here I guess is WHAT is powering the ECU after shutdown? Is it being fed power via X3 pin #2? which is the way it gets power before the engine starts powering itself. Or is it being fed power over X3 pin 1, which is only used in emergency ops, when the EMS Emerg Battery button in turned ON. I think the HIC light may give a clue.
I think you're still safe to fly, but I don't think something's right.