Hi Todd,
The reason the login popup keeps appearing is because of the calendar module. Since the lockdown mode is enabled, whenever the calendar module is trying to load its contents, it produces the popup because the module wants the user to login first.

My suggestion is to set the acccess level of the calendar module to registered only(http://take.ms/uuTbp). When you do this, the calendar module will not be displayed to guest users, thus eliminating the need for the login popup to appear.