Thanks for your feedback, My places are personal artifacts that we are assuming you do not want to remain persisted on the device after you sign out. Could you go into some more details as to your workflow here and why you would need them persisted between multiple logouts?
In general, when you sign out Explorer will delete any information created/persisted by that user. This includes recent search history, recent maps as well as places.
Happy to discuss ways of making places more useful to you and your organization however, so it would be great if you can share your workflows with us.