4670x - Roku Ultra,
Roku TVs (sets with Roku capability built in) already had Settings > System > Power > Power settings > Auto power Savings options, whereas separate Roku devices had only Settings > System. On the Roku TVs this gives two options:
Then in Roku operating system version 10.5, the latest one currently in release, they extended the power saving concept to Roku devices as well as Roku TVs. On some newer Roku devices, they added a Settings > System > Power > Power settings > Auto power savings menu option like on Roku TVs, but it has only one option:
I don't think they did a very good job of thinking through how to implement this on a system where the Roku and TV are separate non-integrated devices.
With a separate Roku device, turning the TV back on when its been off a while just leaves the connected Roku device in low power standby limbo. In its current implementation you can bring the Roku back up by methods already mentioned but you are not told of these methods and there is no way to do it automatically. Today all you can do to avoid this on a separate Roku device is to disable this new power saving feature altogether.
And, of course, this whole thing is complicated by Roku not telling us on which "newer Roku devices" this change has been implemented in the first place. In @rockworm's case, it even sounds like they may have implented it on at least some Roku models without including a menu option for disabling it (??).
We can only hope that in a future update Roku will find a way to correct this (perhaps by extending CEC into a two way function where the TV can fire up the Roku, instead of its current one way function where a Roku remote command will cause the TV to turn on and if necessary switch its input to the one for the Roku.).
My my separate Roku, a newer model, has no power options in settings.