If I don't use the unit for a long time, the power sometimes goes off. Is my unit broken?

No, it's not broken.
This unit comes with an auto power off function, which is enabled as the default setting. The power turns off automatically when there is no signal input, output or operation for approximately 4 hours.
To turn on the power once the unit has turned off automatically, press the power button on the rear panel to release it to the off position, and then press in the power button again.
To disable the auto power off function, press the [GLOBAL] button to display the GLOBAL menu. Then, turn the rotary selector to switch the [Auto Power Off] setting to [Disable].