Mauricio,
I received your email and I'll answer here. With 10.3.1 the only consistent connection you can make to ArcGIS server is with the ArcGIS Server administrator account. The admin account you define when AGS is initially installed. If you have disabled that then enable it again and use it for connecting. I have found this for both logging into the GEE administration tool and for defining the data store. The AGS instance can be set up for Windows authentication and using the Web Adapter so that your map services can be assigned to Windows Active Directory users but I have experienced inconsistent GEE connectivity using a Windows account.
Also, it's important to use the URL generated during the data store registration as described by Javier Delgadillo in the thread https://community.esri.com/message/550574#550574
DG