Sorry, Sluggie, didn't spot that you did say the earlier entry was submitted by djevenden, so I think must be regarded with a pinch of salt.
However, whilst we don't have any evidence that the submitted entry on FamilySearch for Nathaniel John Evenden born in early 1881 does in fact belong to our Nathan and Mary Ann, there is separate evidence of the birth in the official registration, so the child did in fact exist.
And, as you say, this could be one of the missing, dead, four children shown on the 1911 census. We know that Arthur died in 1905, and that Alice died in 1903, so if Nathaniel is another death - although I can't see the death ref, we are only missing one more.
I did do a search of Evenden births/deaths in the gap between Elizabeth's birth in 1892 and Arthur's in 1900, and came across a possible (would need a certificate to prove it), a Polly Evenden, born Oct 1897 in Maidstone and died April 1900 also in Maidstone.
But more interesting, can I ask for help from anyone still reading through this thread?

Where are the following children of Mary Ann and Nathan in the 1891 and 1901?
In 1891 the family were in Woolwich (10 Rope Yard Buildings), and in 1901 in Claygate Cottage, Wrotham, Kent.
Missing from both the above censuses is:
Mary Ann (sometimes called Marian) EvendenBaptism 6th June 1888 (birth 9th May 1888) St Peter's Maidstone
From Familysearch.
Birth Ref Mary Ann Evenden, Apr qtr 1888, Maidstone 2a 713
I only have her in the 1911 where she is Marran Bell. She marries as Marian Evenden in 1913.
And missing from the 1891 census is:
Alice EvendenBaptism 13th March 1890(birth 16 Feb 1890) Woolwich Holy Trinity
Birth ref not yet confirmed.
I have her on the 1901 with her family in Wrotham, and I think she dies in Jan 1903
I cannot see either of them with other family members of her mother - had another good look last night! And I also added some detail to her father Nathan's tree, and his siblings, but couldn't see them there either.
Any suggestions, anyone?