The woman had weird fantasies during her pregnancy. The anecdotal evidence is that lots of women do, so probabilities are that some of them will be true, just as some psychics' predictions come true.

She told the anesthesiologist about her symptoms. Turned out she really did have a problem, and the doctor caught it. That's pretty common, too.

She tells the story in retrospect, saying that she insisted to her earlier doctors, in detail, that something was wrong, and they ignored her. I wonder what she really said to her doctors and her husband. It might be contemporaneous doctors' notes, letters, diaries or well-corroborated eyewitness accounts (not an exhaustive list). In the meantime I suspect that she's making herself look better in retrospect.

As for what Objectivism has to say, Barbara Branden's efficient thinking lectures took the topic up, noting that the subconscious can give us information that we aren't aware of consciously. She illustrated the point with one of Agatha Christie's Hercule Poirot stories. Maybe the present story is an example of this. It isn't a problem for Objectivism.

Simple question here. Did she catalog ALL, or at least a signficant sample of her "premonitions," then count up the hits as well as the misses? Of course not. Is this story even even worth the time to read the title? 

The answer is a very, very conditional "Yes" - the condition being that there are no 'intuitions' as people tend to describe them.  That kind of intutition has to be seen as akin to "ESP" or "Telekinesis" or "Magic."  There are a large number of stories like this but they all want to claim some power or mechanism that reason can't find and they all are based upon 'knowledge' of reality by magical or non-specific means.

We don't need the word "intuition" to explore, scientifically, what we don't know about the flow of data from those senses that we know about to the subconsious and from there to something being presented to the conscious mind.  Epistemologically, this form of the transformation of sensations to a 'percept' needs a way to validate the percept because the subconscious is just as likely to present us with fantasy - How would we know the difference between some valid internal sensory input 'telling' us we have a specific ailment, and a tendency to convert feelings of stress or worry into an imagined concrete illness (hypochondria)?

As a side note, it should be pointed out that when we focus on the senses we usually only discuss those that sense the external world (sight, sound, smell, taste, touch, temperature).  But we have internal sensations as well: hunger, lack of oxygen, build up of carbon dioxide, thirst, spatial orientation, balance, acceleration/deacceleration and gravity, spatial orientation of our limbs, internal pains and aches, and many more.  We have used reason to find the means of measuring and validating what we sense of the external world (e.g., working with color theory, properties of light, perspective, physiology, etc., to validate and understand sight)... we haven't done that much for our internal senses.  Other things seem like we 'sense' them, but are probably products of the subconscious, like the 'sense' of passing time.

There is this divide where on one side there are mystics who are into things like out-of-body experiences, ESP, visions, etc., and on the other side there are psychologists and neurologists and these two sides have such widely differing epistemological bases and such different motivations, that they usually don't work together to explore new territory - such as how much control can one consciously gain over what are normally only subconsciously controled elements in our physiology (e.g., can you consciously 'will' yourself to have 'goose bumps' or to blush?).   I've seen and done things with hypnosis that make it clear that there is a lot we still don't understand and that there is much more that the conscious mind is capable knowing and doing.  I don't, however, believe that this is 'the' explanation for claims of valid intutions - I'm betting that 99.99% of those claims are a kind of wishful thinking, neuroisis, a kind of religious experience, an example of 'faith' - mysticism - take your pick.