Hi there,
Thanks for "Jane" ... here's hoping it helps

You mention five children for Eliza .... Perhaps there were more :
1884 Eliza H MAY birth registered Nymagee with William and Eliza recorded as parents # 18957
1889 Joseph H MAY birth registered Nymagee with William and Eliza recorded as parents # The “V” record
1893 Alice M M MAY birth registered Bourke, with only Eliza recorded as a parent # 7676
1896 Joseph H M HAMPTON birth registered Cobar with only Eliza M recorded as a parent #11785
1899 Nelly L HAMPTON/MAY birth registered Cobar with only Eliza J recorded as a parent #20149
1902 Amy HAMPTON/MAY birth registered Cobar with only Eliza recorded as a parent # 2272
1904 Robert MAY birth registered Cobar with only Eliza recorded as a parent # 2318
A transcript of Robert’s birth registration should include the names of his older siblings and also the then current address.
As I understand it, the rural/regional registrations were meant to be submitted by the deputy registrars by ordinary mail to Sydney on a quarterly basis, BUT sometimes those deputy registrars were very busy on their main duties (usually attached to the court house/police station etc, Sherrif/baliff duties).
Also, the Sydney HO was under funded and quite often the returns were received annually or not received at all. So while it seems out of chronological order, it is possible that the birth for Alice MM on the index as 1893 and the death of Alice 1892 is for the same child, but you would need transcripts to verify that suggestion.
The two consecutive numbers that Sue mentioned earlier may not be for two deaths that occurred at the same time, but simply be for two deaths in the same year, or two deaths indexed by NSW BDM’s HO at the same time.
However, because the wildcard option “ * “ is not currently available at the NSW BDM online index, I have not been able to determine if the registration numbers for all of that BDM district of Nyngan were indexed quarterly or annually. I hope that my ‘brief’ explanation of that admin process makes sense.
Cheers, JM