The Office Software Protection Platform service is generally started on demand when a user has started Office, however, there are license types which can start the service otherwise (such as those using a Key Management Server). As for stopping the service, there are several reasons we do not automatically shut down the service by default. These reasons are based on Office's cross OS version compatibility, communications from our users about their Office usage profile, preferences, resource usage profile, and differing ways in utilizing the service between Office and Windows.
That said, while we do not default our service to timing out after inactivity, if this is something your organization values, you have the ability to control this. You may set the following registry key:
Key: HKEY_LOCAL_MACHINESOFTWAREMicrosoftOfficeSoftwareProtectionPlatform
ValueName: InactivityShutdownDelay
ValueType: DWORD
ValueData: The number in seconds, that the Office Software Protection Platform will stay running for, after the most recent activity. The windows default for this is 300 seconds.
After setting this key, simply restart the Office Software Protection Platform Service to use the new settings.