This Homam is done to worship the god of life (Ayur Devata). By doing this Homam, one gets long life blessings from Ayur Devata. Sage Bodhayana explains Ayushya homam in the Bodhayana sutras.
According to him, if a child is constantly ill, this Homam could be performed on a monthly basis until the child attains good health. But in general, this is performed once a year on the day of the star in which the child is born. It is started on the day the child completes one year of age. In case one is unable to perform it on this day, it should be done on the consecutive month. It may be done even on a monthly basis.
You will need to perform this Homam on the Star (Nakshaktra) birth date of the child. It is very important that you do it on the first birth day. Optionally, you can perform it on the other birthdays too.
By performing the Ayushya homa, the evil effects caused by tithi [day of the fortnightl], vara [day of the week], nakshatra [star] are eradicated. It bestows longevity and good health.