If not plugged in directly to the TV, what is the stick plugged into? If it's an HDMI switcher, that might be causing this, if that's the "middle man" here. You could always use a short HDMI extender, and velcro the stick to the back of the TV. Any other cables in the equation should be swapped for new ones, one at a time. Even if they're "good" cables, they may just not like playing nicely with the Roku Stick..
Yeah, I got some Rokus.
https://youtu.be/d1CSEeqWl10