West Sussex families frequently move across the county boundary into Hampshire. If your West Sussex family has disappeared, this may be the explanation.
Records relating to the County of Hampshire are held at Hampshire Record Office in Winchester. I no longer visit Hampshire Record Office.
Copies and transcripts of Hampshire parish registers, Bishop's Transcripts and monumental (gravestone) inscriptions are also held by the Society of Genealogists' Library, which I visit regularly.
Please contact me regarding searches of Hampshire sources held in the Society of Genealogists' library. Please provide all relevant details in your e-mail. I regret that I'm unable to offer a free initial assessment if I'm asked to visit your website to locate information.
Hampshire newspaper searches can be undertaken at the British Library.