I have a Roku Streaming Stick (3600 series), with its USB cable connecting to a Raspberry Pi (if you don't know what that is, it's a small computer, I previously used the Nintendo Switch dock).
Sometimes, it works perfectly fine, but sometimes, both the remote (sans the power and volume buttons) and stick cease to function, and assumes it's connected to the TV's USB port. (it annoys me because it usually happens in the middle of a video I'm playing on YouTube)
Because you also can't use a phone to control the device, the only way to fix this is by turning off the Roku, moving it to another USB port, and powering it on.
The USB cable on the Roku 3600 is simply for providing power to the Roku device.
It really can't assume anything (it doesn't know where it is drawing power).
You can try using a longer micro-usb to USB-A cable and then a 5volt, 1amp USB charging adapter (like a cell phone charging adapter) and plug it directly into the wall outlet and see if that resolves your issue.
Roku sells a 5ft cable, but you can find them in just about any electronics dept in a store. https://www.roku.com/products/accessories/roku-micro-usb-power-adaptor
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Your Pi may be either entering into a sleep mode/suspend mode that is cutting power to the Roku device. Depending on the build and model, you may need to look at the Sleep, Idle, or Halt settings. You can try adjusting the Pi's power settings if you wish, or just use an alternative power source to provide continuous power to the Roku device.
Adding to the reply from @AvsGunnar ..
The USB ports on many televisions only supply 0.5 amp or less, which is not enough to power a Roku reliably. A minimum of 1 amp is recommended. It may appear to start up okay, but when it runs into something that requires more power than the TV's USB port can provide, something's got to give. In many cases this results in shutting down the stream you are viewing and exiting back to the Roku home screen.
If this is a new problem, possibly an update to either the Roku operating software or to some channel app software is using a little more power than in the past. If you were just barely scraping by before, this might push you over the edge.