Are you sure it's getting power while you're using it? It sure sounds like the cord is intermittently off. Maybe the cigarette lighter plug part (assuming you're using a 12V cord) isn't fully seating in the socket; they can be rather persnickety at times. It's also possible that the connector on the GPS end isn't seated well or the wire has a poor connection from being bent too much there.
In general, if the GPS is sometimes complaining of and acting like it's running on (and running out of) battery power, I'd tend to believe it unless I had very good evidence to the contrary.