From support pages:
"You can enable CEC on your Roku player from the Settings menu using the steps below.
- Press Home on your Roku remote
- Scroll and select Settings
- Select System
- Select Control other devices (CEC)
- Highlight 1-touch play
Check the box to enable 1-touch play"
I would think you'd want to disable it, but changing whatever state you find it in would be worth trying.
Also:
"You can use the following steps to disable auto power savings.
- Press Home on your Roku remote
- Scroll and select Settings
- Select System
- Select Power
- Select Auto power savings
- Uncheck the box next to After 20 minutes of no interaction
After you disable auto power savings, your Roku player will remain "awake" and ready to be used any time your TV is powered on."
Those are the two things that come to mind that may make a difference.