Sorry for the late reply -- I hope you're still out there..
Starting with Roku operating system version 10.5, Roku added a "Power" item in the "Settings > System" menu for some of the newer Roku devices. The new "Auto power savings" item there will put your Roku device into a low power standby condition after a period of inactivity, such as when your TV has been turned off for a while.
Pressing a Roku control key (like the Home button) on your Roku remote (not Power, Volume, or Mute buttons if your remote has them, as they act on the TV, not the Roku) should bring the Roku out of standby and back to full operation. Pulling the power for a few seconds to restart the Roku will restore full operation as well.
If you disable "Settings > System > Power > Auto power savings" it should prevent your Roku from going into standby in the first place. The power savings are not that great and for the hassle it causes, I don't think it's worth having this feature activated.