Can a USB keyboard turn off due to lack of PSU power?

Question

Keyboard

The Logitech G810 (500mA) keyboard worked fine for several months.
Then I added an A4Tech Bloody R70 mouse (via a native usb extension cable).
After some time, the keyboard began to turn off (and does not turn on).
When you try to reconnect usb (it doesn't matter to the same or to another port), it says "device not recognized".
When connected to another PC, sometimes it starts working, sometimes it doesn't.
If, by connecting to another PC, the keyboard worked, then when you turn it on in your native PC, it also starts working.
The service said that the keyboard is working and it's in my PC.
I doubt it very much, but still, purely theoretically, can a power supply be missing?
UPD
It looks like it's all the same in the motherboard (ASrock ZH77 Pro3)

Answer 1

They did NOT do anything in the service, I had to disassemble the clave myself.
The reason was in poor contact .
The wires were very weakly held in their socket (dangling back and forth)

Answer 2

Logitech G810 (500mA)

Many mothers have a current limit of 500mA (that's the USB-2 specification limit), but in my experience, there's always some headroom. So hardly.

(via native usb extension cable)

What is a "native extension"? If it’s just a wire, then it will not affect anything - the connected device will remain alone, the current will not increase. If this is a hub-splitter, then connecting another current consumer will increase it beyond the 500 mA limit, and a shutdown is possible (and the hub itself, even empty, consumes some).

When you try to reconnect usb (it doesn't matter to the same or to another port), it says "device not recognized". When connected to another PC, sometimes it works, sometimes it doesn't.

This is very similar to a break in one of the signal (not power) wires. A few months of intensive use may well happen. Diagnostics: probe the entire wire, twisting and squeezing it in sections, simultaneously poking the keys and watching the input on the screen - sometimes it’s possible to find a defect this way. Most often, it happens at the cable exit from the case and from the USB plug - check these places very carefully. Instead of diagnosing, you can try to stupidly solder the entire cable to a known good one.