I just added a Roku Express 4K+ to my home theater. The HDMI signals are sent through an HDMI switch which takes input from a DVR, a standard DVD/CD player and a PC Laptop as well as the new Roku,and sends it to an Epson 2040 projector.
Whenever I switch input from the Roku to one of the other devices on the HDMI switch, the Roku seems to go to 'sleep' in about 20 minutes and sends a signal that turns off the Epson Projector. When I turn the projector back on, it wakes up the Roku and the whole 20 minute cycle starts again.
Roku operating software version 10.5, currently rolling out, adds some power management controls for some Roku models via Roku menu path Settings > System > Power. I think the Express 4K is one of those models.
I haven't received Roku 10.5 yet, so I'm lacking details. If you have a Power option under Settings > System, see if any of the settings there take care of your problem.