Elisabetha was born 22 December 1577 to Johannes Sidler and Magadlena Stälin and was baptized.
Stillborn/baptism: Stillborn children or children who had died before baptism were not allowed to be baptized. But perhaps not all pastors adhered strictly to this if the parents had requested it. With regard to stillborn children, I (in a Reformed congregation) also assumed this. Catholics were probably more concerned about the salvation of these children - including the use of a baptismal syringe for the emergency baptism of unborn children. In the article Unbaptized deceased children in the early modern period I read
According to church doctrine, children who died without being baptized still bore the stain of original sin. Without baptism, they were denied both a dignified burial, ritual books forbade a church funeral with prayers (the "Rituale Viennense", 1774, clearly counted the "infantibus mortuis absque Baptismo" among those deceased, "quibus non licet dare ecclesiasticam sepulturam"), as well as a blessed abode in the afterlife. Their place of residence was the "Limbus puerorum". A place between heaven and hell, from which there was no redemption. Unlike in purgatory, the bereaved were unable to change the children's fate for the better, even through prayers and almsgiving. It was not only Martin Luther who railed against this rigorous and seemingly implacable attitude of the Catholic Church in his comments on the subject of baptism; other scholars and theologians of the new denomination were also sometimes harshly critical of this strict concept of the afterlife. According to Protestant belief, it was by no means mandatory that an unbaptized child could not go to heaven. see Geneal-Forum.
Life expectancy
Average life expectancy at birth for English people in the late 16th and early 17th centuries was just under 40 – 39.7 years. However, this low figure was mostly due to the high rate of infant and child mortality; over 12% of all children born would die in their first year. With the hazards of infancy behind them, the death rate for children slowed but continued to occur. A cumulative total of 36% of children died before the age of six, and another 24% between the ages of seven and sixteen. In all, of 100 live births, 60 would die before the age of 16. A man or woman who reached the age of 30 could expect to live to 59. [Thomson Gale, 'Infant Mortality' (1998)]
Food shortages and insecurity were leading concerns in the 18th century, especially in Europe, and these were exacerbated by reduced harvests yields. Disease was another leading cause of death, with rats and fleas being the common carriers of disease, specifically plagues, during this era. (Wikipedia)
Common diseases were dysentery, malaria, diphtheria, flu, typhoid, smallpox and leprosy. (Wikipedia)
Death seen as natural
If a woman died after the birth of a child (this was a dangerous process because of infections), her younger sister stepped in as new wife, or replacement. The husband (here farmer in the country) absolutely needed a wife to look after the children and farm house (cooking etc.). So he normally got remarried a second, or third time within a few months; later a one year period was recommended. Often these wives were widows themselves. So there was constant giving births and dying on the farms, similar to what happened in the stable with the animals. Death was seen as natural. Only medicine and hygienic measures lowered the infant and childhood mortality rate. However, there were very bad pestulenza waves in the 17th century in our regions. Many villages lost 30 to 40% of the population. (Peter Bertschinger)
Julius Billeter
We often see that from the age 20 years on, when marriage was allowed by the church, the parents had at least one child every year, often stillborn. The rule for naming was that the godparents gave their first name to the child. For example if a child named Jakob died, they continued the name until one survived the first years. From this Julius Billeter, Swiss genealogists, concluded that a child died young and noted a "dy" by their name. On average these big farmer families had about two boys and two girls that made it to adulthood and most of them got married. (Peter Bertschinger, FamilySearch)
Elisabetha Sidler birth 22 Dec
1577 film 8014328 page 41
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22 Decembris [1577]
E(ltern): Hans Sidler, Madalena Stölin
K(ind): Elisabeth
Z(eugen): Mich(?)l Sigerist, Margareta Schiller
Mich(?)l: not sure about this letter - but only Michael makes sense.
Note: You mention "… is assumed to be a stillborn." I don't think a stillborn child would be baptised. In some records there are separate sections mentioning stillborn childen - if listed in the baptismal register I would expect a corresponding note. Possibly Zürich was an exception - see Geneal-Forum.