I was experiencing the start engine issues with my Honda Fit 2015 for months. It usually takes 10-20 presses on the push button before the engine can get started. In the meantime, the immobilizer indicator light also stays on after the engine when the engine is running. So I guess the push-button issue is related to the immobilizer anti-theft system. Before going to the dealer, I gave it a last try by disconnecting the battery. And it works.
Please note that this is a temporary fix. If the problem happens again, you should consider replacing the push start button. Contact Honda dealer for more information. It seems that they have extended the warranty for this part to nine years.
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