Lot's of good tips from Eggman. This might be a simple interference problem from a secondary device.
Does the owner's manual explain the car's "Immobilizer System" (this is what Mitsubishi calls their anti-theft system)? When the computer doesn't detect the proper ignition key for any reason, it will prevent the car from starting. Usually when this happens in most cars, some sort of security light will blink or illuminate on the instrument panel to indicate a problem. If this is the case with the Mirage, see if this light is illuminated the next time your car doesn't start. I think this is what the immobilizer light is...
There is a whole section in the service manual on the immobilizer. I just read it briefly, but it seems to indicate that diagnostic codes are stored if a key fails to start the car. I wonder if the dealer is able to tell that?!?
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View my fuel log 2015 Mirage ES 1.2 manual: 52.2 mpg (US) ... 22.2 km/L ... 4.5 L/100 km ... 62.6 mpg (Imp)