When you use FaceAlpha, that forces the use of the OpenGL renderer. Without it, you are getting the Painters renderer. OpenGL can have difficulty when the axis values are very close together.
If you do not need to use a DataCursor, the workaround is to shift and scale the values you use for the X axis so that they are numerically further apart, then set the XTick according to the shifted and scaled values, and then set the XTickLabel property according to what you would want the user to see at those locations. For example you might datevec() to extract the hours, minutes, seconds for the places you would like ticks, and sprintf() the parts together to get a tick label.
