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Like passports, your green card also has an RFID chip in it, which allows for machine reading. Occasionally, these chips stop working. If this chip is broken, then the Automated Passport Control kiosk will always reject it. The referral code printed on the X receipt should be TR in this case. The Android app ReadID can read the chip in passports and green cards, so you can tell for yourself if the chip is working or broken. (I'm not aware of an iOS app which can reliably read passport/ID chips.)
Since USCIS started issuing green cards with RFID chips in mid-2010, and your card was issued in 2010, it's also possible that you received one of the last cards without a chip.
In either case, if it really bothers you, you can get a replacement green card. But since that costs $455, you might want to wait until you have to replace it anyway at its expiration. Or you may be able to naturalize as a US citizen, but that's a topic for another site...