Those vector shapes have the same stroke configuration, and on the pointy end there's only 1node.
So why this happens?
The Miter Limit for the corner.
The Stroke Panel has a field to adjust the miter limit titled "Limit". If the angle of the corner falls below the limit, the corner is butted rather than mitered.
If you increase the miter limit, you'll see more miters appear.
I'm not 100% certain what the number actually relates to (what unit). I think it's degrees of angle. So, an angle of less degrees than the Limit does not get mitered (it may be 'more than' however). I really haven't tested it thoroughly enough to understand the direction of change. I merely know to change the Limit field if I'm not getting miters when I want them. A minute change of .5° in the angle can be the difference between a mitered joint and a butted joint.
What is happening is that the angle of this point is creating too large of a cap for illustrator to display properly. You must either widen that angle or consider using a rounded point.