i have a similar problem with my 3 week old 350. i have it powered to a switched 12v accessory lead on my 2011 concours. The unit worked fine until while riding the other day, it lost power and showed the count down to shutting off and then would regain power when the countdown reached 2 seconds left. It continued to go through this cycle of power/no power over and over again until i just shut it off altogether.
I checked and rechecked the connections to the hot lead and ground and checked the voltage from the leads... everything was fine with those.
Now, when i turn on the ignition, it powers up. But, when i turn the bike off, it does not power down like it should and just switches to the internal battery.
The gps functions as it should when i have it plugged in to the cig adapter in my car.
This doesn't necessarily mean the bike cradle or the power supply cable are bad as the connection in the car to the unit is a usb type connection into the back of the unit.
I did not, however check the voltage at the two leads on the cradle that match up with the ones on the gps, as mentioned in a above post.
I called Garmin and they suggested i try a new power supply cord (they would send me one under warranty) but i insisted they send me a new unit as they couldn't tell me with any certainty that would fix my issue.
I guess this is what i get for buying a brand new unit to the market.
Garmin tells me this is not a known issue with this unit, but after reading the above posts.... it makes me wonder.