Hi,
There have already been several threads on this issue. You say you still have tvOS 9.1.1. Is this true, or are you actually on 9.2, like most of us?
There does appear to be some problem in the tvOS software that causes this, but the solution is unreported as yet. And the problem is not universal. It affects a subset of ATV users.
Could there be interference on your network (noisy neighbors) while ATV is sleeping? That might knock it into the state you see.
You should report this at http://www.apple.com/feedback/appletv.html just to add weight to the problem.
This Get help with Wi-Fi networks on your Apple TV - Apple Support reviews the steps to check that your WiFi is working as well as you think.
For what it's worth, I thought it might be that the sleeping ATV was failing to renew its DHCP lease. But I left mine sleeping for 39 hours, much longer than the lease value of 24 hours. And it woke up absolutely smoothly, connected to YouTube, etc. So either it retained the lease, by renewing it periodically, or it woke up and easily obtained a new one. The Netgear genie app and independent NetworkAnalyzer app reported that it was still on-line at the same IP at the end of the sleep interval, which suggests that it stayed on-line.
Have you by any chance configured more than one WiFi network? I suspect it's meant tp work like iOS and connect to whichever network it finds. But that may not be working. If you have configured multiple networks, you could try reducing it to one, and report back, please.