I have the same problem with being randomly logged out of the desktop app for QBO. One of the big selling points of the app was that we were to be able to stay logged in so that we could work on our various clients' books throughout the day without having to login constantly. 

In my case, it doesn't even track the three hour interval. Sometimes it will log me out in the midst of making entries (as other posters have reported) but at other times, it will keep me logged in all day. 

Please, please fix this.