Hi Mike,
Currently, it is not available to disable the feature ‘Keep me signed in’ in Office 365.
However, based on my test, when you already open a site in SharePoint Designer and clicked “keep me signed in”, you can open another browser, and sign in Office 365 using a different tenant Office 365 account, then open another site in SharePoint Designer. Maybe you should type the credential again when you open the site in SharePoint Designer.
Thanks,
Linda Wang