Researchers from the Danish Epidemiology Science Centre found that the deaths of kids fathered by over-45s occurred at almost twice the rate of those fathered by men aged between 25 and 30.
They believe that the kids of older fathers are more likely to suffer particular congenital defects as well as autism, schizophrenia and epilepsy.
According to researchers, the findings are linked to the declining quality of sperm as men age.
For the study, a total of 100,000 children born between 1980 and 1996 were examined, of whom 830 have so far died before they reached 18, the majority when they were less than a year old.
The deaths of many of the children of the older fathers were associated with congenital defects such as problems of the heart and spine, which boost the risk of infant mortality.
However, there were also higher rates of accidental death, which the researchers believe might be explained by the increased likelihood of suffering from autism, epilepsy or schizophrenia.
Until now, most research into older parents has focused on the risks passed on by older mothers.
However, the new study was adjusted to take account of maternal age and socio-economic differences.
The research also found higher death rates among children of the youngest fathers, especially those below the age of 19.
However, the study said these differences were explained by the risks of teenage motherhood and poorer diet and lifestyle.
Earlier studies using the same data found that older men were four times as likely to father a child with Down's syndrome, while other studies have found that the genetic quality of sperm deteriorates as men age.
"A lot of people know that there are risks for the child that come from having an older mother, but children of older fathers also carry an increased risk. These sorts of results provide another good reason to have children early, when possible," the Telegraph quoted Dr Allan Pacey, senior lecturer in andrology - the medical specialty dealing with male reproduction - at the University of Sheffield, as saying.
Pacey said scientists were unsure exactly what impact the ageing process had on the quality of sperm, making it impossible to detect defects before conception.
Dr Jin Liang Zhu, from the Danish Epidemiology Science Centre, which carried out the research, said: "The risks of older fatherhood can be very profound, and it is not something that people are always aware of."
The study is published in the European Journal of Epidemiology.