Well that was fast: Apple just released iOS 10.0.2, with the update's release notes confirming that it fixes an issue that caused Lightning headphone controls to be disabled after a period of inactivity. The bug was reported soon after the iPhone 7's launch last week as customers began getting acclimated to life without a headphone jack. Apple said it would address the problem with a software update, and to the company's credit, that happened very, very fast.
Any physical controls that are part of your Lightning-connected headphones or earbuds should now keep working even after you've stopped listening to anything for awhile. It's yet another example of the benefits of Apple's total control over iOS. Annoying bug gets discovered; annoying bug is resolved within a week for all users on iOS 10. Not bad, Apple. Not bad. iOS 10.0.2 also addresses two other bugs: the first caused Photos to quit when some users switched on iCloud Photo Library, and the other fixes "an issue that prevented enabling some app extensions."