Death when the promise of life is so great is death at its most unfair. The first steps that won’t be seen. A first word unimagined. These losses are a darkness. A pain leaving a vacancy where a full heart was supposed to have been.

There was little in the way of formal Jewish ritual to comfort parents either. Before the age of modern medicine, fevers, infections, and common illnesses that we regard as minor overtook many children before they reached their bar and bat mitzvah.

My grandfather had a younger sister I never knew. My mother had an uncle who caught a chill after a bath and passed away before his brit milah.

A Summary of the Halachot Regarding Still Birth and Infant Loss Traditional Jewish law is that if a child dies before reaching the age of 30 days, no formal burial is required. Such a child is considered a nefel, and for such a child, no burial and no mourning rites are required (Ket. 20b; Shab. 135b; Evel Rabati I; etc.)

The Shulhan Arukh addresses whether a eulogy is permitted; it says for the children of the poor, it may be done from the age of five and onward; and for the children of the rich, from six and onward (M.K. 24b; Shulhan Arukh 344.4).

This shows that, traditionally, little was made of infant deaths. Further, a nefel was treated as an amputated limb, and buried in the general section of the cemetery (Ket. 20b) to avoid ritual uncleanliness for the priests (M. Edut 6.3; Yad Hil. Tumat Hamet 2.3; Pahad Yitzhaq, Ever).  Note that, strictly speaking, it was not necessary to bury amputated limbs (Shulhan Arukh, Yoreh Deah #209).

It's very easy to think of the traditional position as "heartless." When you've lost a baby and need to grieve, it's natural that you'd want to do it in the way you're familiar with. Orthodox families in this situation are usually forced to look for alternative ways of coming to terms with their grief, since in most cases, the traditional funeral and mourning periods are not observed.

This doesn't mean that nothing has happened, or that as far as Judaism is concerned, they have not experienced a loss. They still need consolation and any compassionate Orthodox rabbi and community will recognize this and do their utmost to help the family through their time of pain. (soc.culture.jewish FAQ)  

Finding others who know your pain, at support groups, through counseling, is paramount. Rabbis and obstetricians can make the connections to helpful agencies and counselors.

Recommended Reading

Tears of Sorrow, Seeds of Hope by Nina Beth Cardin
Many people who endure the emotional suffering of infertility, pregnancy loss, or stillbirth bear this sorrow alone. The sorrow of the emptiness felt from a loss that is without a face, a name, or a grave. At last, there is a source that acknowledges and encourages expressions of their grief, and offers comfort in the moments of their pain.

When a Baby Dies by Nancy Kohner, Alix Henley
Using letters from and interviews with many bereaved parents, Nancy Kohner and Alix Henley have written a book which offers understanding of what it means to lose a baby and the grief that follows.