I too have a few unregistered births and deaths in my family tree. One from the Adelaide Hospital!
According to Beryl Schahinger's book"South Australian Registration Districts of Birth, Deaths and Marriages"there were many reasons why a BDM was not registered.It explains how registrations were made and then forwarded to the Principal Registrar in Adelaide. It should be available in genealogical libraries.
SA was divided into a number of Registration Districts and BDM's were registered within that district. Copies were made of these district records and forwarded quarterly to the Principal Registrar in Adelaide.
I would imagine that the odd district record did not make it to the Principal registrar for all kinds of reasons.Also that records do exist but have been missed or errors have occurred while being indexed over the years.
According to Beryl's book, no dead body was to be buried without a certificate of registry or of inqest. A form had to be completed by the district Registrar and given to the undertaker who passed it on the to the person conducting a funeral. Anyone who buried a dead body without the correct form was supposed to give notice to the District Registrar within one month. Without a death certificate a name would not appear in any death index. Also Beryl has written that names were sometimes just overlooked.