I'm replying to my own post - I noticed that I HAD changed a setting in BIM Server Preferences, Email Options, Mail server (SMTP) to something that must not have worked. After deleting it and leaving it blank, everything work!
We don't even use email communications in BIM Server, and it shouldn't have an effect on the operation of the Server, and wether or not I stay online or not. Must be bad programming in the server software.
So, I'm staying online for now.
Rick Newton, Architect, ArchiCAD 17, 27" iMac:•3.4GHz Core i7 •32GB 1600MHz DDR3 SDRAM-2X8GB •3TB Fusion Drive •NVIDIAGeForce GTX 680MX 2GB