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That is normal. It is designed to work that way. The idea supposedly was that if you open the drivers door you probably disarmed the car on purpose. The car will relock itself if the drivers door is not opened. The reasoning behind that was if you accidently disarmed the car while walking away and putting your keys in your pocket, the car will rearm and lock automatically for you. All the Honda/Acura keyless entry systems that were of the era that the NSX system is act the same way.