Clear the device's memory: A few users claimed that, when trying to pair an iPhone 5 to their car's audio system, the system would instead continue to attempt to connect with a previously paired, now absent, iPhone model. To fix this, wipe the car system's memory clean, having it "forget" all previously paired devices. After doing so, pairing with the new iPhone should succeed.
Update to iOS 6.1: In some cases, the culprit may be a bug in the iOS 6.0 software. At least for Honda CR-V owners, upgrading to iOS 6.1 seemed to eliminate Bluetooth pairing problems.
Consider the hardware: As it happens, my wife's iPhone 4 fell victim to an intermittent Bluetooth failure. About half the time, the phone would successfully pair with the aftermarket Sony Bluetooth audio system in her car. At the other times, the iPhone would fail to pair. None of the above suggested solutions had any effect. What did work was dumping the iPhone 4 and moving up to an iPhone 4S. In this case, I suspect there was a Bluetooth hardware failure in the iPhone 4.
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