The 1st Apple KB article linked by @SE56 specifically distinguishes the troubleshooting for the different remote models. The described procedure describes how to restart the remote… not the Apple TV.
I know from personal experience those remote sometimes act up. I once had a ticket with Apple where they suggested I buy a new remote (and later a new Apple TV). If you google for issues with the old remote, you’ll find too many such issues.
I’ve not had that such issues with the new versions (fingers crossed).
I know, that’s not helpful… the 1st troubleshooting link can sometimes fix things though; just stick to the guide.