Hi,
Check the Auto Power Off setting in the Power Management settings of your camera.
The default setting is 2 minutes. I think that when you change this setting to OFF that you have to use the off switch to turn it off, otherwise it turns itself off dependant on the setting selected, irrespective of the off switch.
Here is a link to the User Guide,
On the right side of the page click on ''The Setup Menu'', then scroll down to ''Power Management'' for a description of ''Auto Power Off''.
http://fujifilm-dsc.com/en/manual/x100t/