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The issue, which I've also experienced a few times while testing the iPhone 7, happens after you've left the EarPods plugged into the iPhone 7's Lightning port for a few minutes. Audio continues to play, but the volume control dongle stops working, meaning you can't adjust the volume, activate Siri, or answer calls.
It's unclear if the problem affects third-party Lightning headphones.
The glitch doesn't happen every time. It's seemingly intermittent and random. (I thought I was going crazy until I saw some people with similar issues complaining on Twitter.) If you experience the problem, you can just unplug your EarPods and plug them in again to temporarily fix it.
An Apple spokesperson told me the problem will be fixed in a future software update.
Apple removed the standard headphone jack in the iPhone 7 in favor of wireless headphones or headphones that plug into the Lightning port. However, the Lightning port is a more advanced kind of plug, and it's partially controlled by software. So if there's a bug with the software like there is in this case, your headphones might not always work properly.