QB Issue Resolution:

That would happen in qbo, but in desktop, you have to manually log off.  there is no setting for automatic logging off after a specific time.

Resolution for Issue 'logoff company file after inactivity' available: Yes (Solved).
Source: Intuit Community forum.

logoff company file after inactivity: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

Support for after inactivity
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Error Recovery for after inactivity [Canada]
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