Hit the zoom button once and the polyline disappears. I don't know why. I do know that the API documentation indicates that zooming in can only make a point more likely to be plotted. Thus I consider this to be a bug in the API. See the map below for a rough fix.
The map below, which seems to work fine, is almost identical to the map above. The only difference is that the zoomFactor has been changed from 2 in the top map to 2.1 in the bottom map. I have no idea why this should make a difference.