Is there a word that describes the phobia that your child is going to just die in their sleep?

I'm pretty sure all parents have checked on their kids while they were sleeping just to make sure that they were still breathing. My wife will actaully ask me to do this, especially if my kids are sick, or they've been napping for too long.

"Will you go check on them and make sure they're still breathing?" - My Wife

Is this an actual phobia? Does it have a name?

Is this an actual phobia? Does it have a name?

Yes, it is an actual phobia, and it is not very rare. It doesn't have a particular name; it's just an irrational fear (the term death anxiety might apply, though this more commonly refers to one's own death.)

About irrational fears

Obsessive Compulsive Disorder (OCD) has a worldwide prevalence of about 2% (diagnoses; the actual prevalence may be significantly higher), and is characterized by two things: obsessions and compulsions.

Very basically, obsessions are ideas that are uncomfortable because they are unreasonable or intrusive, and compulsions are repetitive actions that people do to quell a fear or prevent something bad from happening, but only brings temporary relief. One can have OCD without either obsession or compulsion, but OCD without obsessive thoughts is less common.

The incidence of obsessive-compulsive tendencies is much higher. It is very common but is not classified as a disorder unless it actively interferes with someone's life.

It's possible that your wife has a mildly obsessive fear that her children can die even though the likelihood is very low. This is exceedingly common in first-time parents of newborns, probably partly due to SIDS being brought to the forefront of public awareness in 1979-80, and further intensified by the frightening discovery that what doctors had been advising (prone positioning of infants) was wrong, and that apnea monitors played no role in prevention. This is enough to scare anyone. But as the children grow, it usually dissipates.

Other reasons people may have unnatural fear of a child's death are if there was ever any significant threat of loss, or loss of a child, parent or sibling. A mother who lost a parent (death, divorce, or other), had a complicated pregnancy, or delivered a premature baby, for example, may have an exaggerated fear for that baby's health. There are a host of similar fears.

Honest and accepting discussion with your wife may reveal this to be an occasional thing, or it might be an actual irrational fear that she handles very well.

To my knowledge (and quick Google check), no, there isn't an existing name for it.

However, the fear is extremely common.

It can be referred to as anxiety or fear over your child possibly dying, outliving your children, or fear of SIDS (Sudden Infant Death Syndrome) in infants.

Something to point out is that the term phobia implies an irrational fear that somehow distresses or impairs you. While I'm not a doctor, I would not classify as checking one your children while they're ill or napping excessively as behavior that adversely affects your well-being. That behavior isn't any more irrational than buying a baby monitor. In fact, physically checking on your children in these situations could be considered responsible. For infants, in particular, it's common to check them frequently at night to ensure they're sleeping soundly and in a safe position.

To be a phobia, the parent would likely have to spend an excessive amount of time and effort making sure there child doesn't die in their sleep.

While I'm sure there are some cases where there is genuine phobia-like distress in parents as it pertains to the possibility of their children dying in there sleep, I doubt it's common enough have it's own name.

I also think that the terms for many phobias were created earlier in the development of modern medicine and psychology. Now, the practice of diagnosing a phobia or other anxiety disorder doesn't require such specific technical names. They can be classified as specific (or situational) phobias.

If a term does exist, or develops, I would expect it to be a socially-created, rather than a clinically-created, term.