The probability is low that all 3 LED's failed at the same time. I suspect that the issue is that the wiring harness has come unplugged or been cut. I am a dedicated DIY're but with a new car under wrarranty I wouldn't bother with the manual in this case, just take it to the dealer.
As bankerdanny stated, there is a seriously low chance that the LEDs themselves failed. This is either a wiring problem, or a computer glitch (since approach lighting is controlled by the car's computer).
@unionbuster: BMW, Audi, Mercedes and any other 'serious' competitors suffer from these issues too. This is simply an example of the kind of issue that happens with a new model the includes a product that is relatively new to the manufacturer.
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