I'm curious to know the source of info for the districts and years you have given for these Sussex births, for there does not appear to be an exact match on the FreeBMD website. Although the two parishes you mention were in the Cuckfield district, Henry & Charlotte's births were registered in Lewes, and had Edward as a second name been acceptable, his birth would have still been 2 years adrift.
Jacob Perry and Annie Bonieface married in Portsea in 1870, so unless Annie had a child before their marriage, your Henry born in Sussex was their first born.
This is his birth and those others officially registered around the area that your Perrys were said to lived in between 1870-1881.
Perry births in the Lewes District
Births Sept 1870 = Henry Charles Yours
Births Dec 1872 = Frederick William
Births Sep 1873 = Charlotte Annie Yours
Births Jun 1874 = Francis Walter
And in the Cuckfield district you only have
Births Jun 1887 George Edward Perry Not your Edward for a reason given below.
The 1881 Portsea census shows the mother Annie with Henry, Charlotte & Edward, but on that census, Edward's birth year and birth place are shown as Portsmouth in 1880. FreeBMD confirms the birth of Edward Thomas Perry in Portsea in Sept 1879 which suggests the family moved to Hampshire a little earlier than you thought.
The other two Sussex Perrys (Frederick & Francis) are not with your family and nor are they listed as having died in Sussex or Hampshire, so it rather looks as though your missing child was born post 1880.
Regards Roy G