Yes. The GX-10 contains an Auto Off function which shuts off the GX-10's power automatically when it has not been used after 20 minutes by default. This setting can be disabled if desired.
If you don’t want the unit to turn off automatically, follow the procedure described in "Making the power automatically turn off after a time (AUTO OFF)" to turn this setting off.
Note that when the setting is turned off, the unit may consume more power.