I did contact Garmin thru local website. They have a nice tool to support the product.
They immediately isued an RMA.
Meanwhile I did contact you guys here and got the info the problem could be the contact pins. Got home and applied some pressure on the mount pins using only the fingernail.
Next day I mounted the GPS on it and went for a ride. Just for the sake of it, loaded the device with POIs, routes and other stuff from Mapquest. After four hours of fun on and off road nothing wrong happened with the Zumo 390.
So I assumed the pins might (probably) got stuck with some dirt and got back to work when I pressured them.
I did ask Garmin to send a new cable only. But they said "this aproach is not listed on their book, so I had to send them all the stuff (GPS, cables and mount) so they could check it). IMHO it´s not worth the trouble disassembling a neatly mounted GPS and cables. So I will took the chances. It still has three additional months on warranty. So I hope I do not need to contact tem again.
Thanks for the help folks!