Back by popular demand, Auto-Save is now available in FlowJo v10.6 . By default FlowJo v10 will not automatically save workspaces.
To turn this functionality on, simply visit the Workspace section of the preferences and choose a time frame for the auto-save to cycle (in minutes).

This will keep saving the workspace, automatically, wherever the initial save was produced.
Note: this function is not available for ACS formatted analyses.