From the estate records, Robert died without a will. The value of his estate was $25. In 1902 is widow Mrs.Elizabeth Zercher & son Doctor/Docton McDowell Zercher were living in Lumberton Co. NC.
Robert could have died just about anytime before 1902. I'd say he died before the date of the 1900 Census where Bettie is shown as a widow. Deaths weren't recorded in Robeson County until 1913, therefore, you won't find a death record for him.
The Rebeson County Public Library, http://robesoncountylibrary.libguides.com/RCPL/genealogy
might have his death notice in a newspaper but I don't know if they'll search without a death date.
He was probably buried without a tombstone and it might be impossible to find where he was buried. You can contact the Robeson County Historical & Genealogical Society
PO Box 2292
and ask if they have cemetery inventories.
I didn't find any other info about Robert in Ancestry nor in FamilySearch.
Born: abt. 1834, South Carolina
Father: Henry Buffet, b. SC
Mother: Sallie Buffet, b. SC
Informant: Dock Zurcher, Lumberton
Died: 12 Nov 1914, Lumberton, Robeson, NC
COD: Cardiac dropsy
Buried: Gun Cemetery, Nov 13, 1914
Mrs. Betty Zurcher, 80 years, died last Thursday at her home at National cotton mill. The funeral was conducted Friday, 11 am, by Rev. W. D. Combs, pastor of Gospel Tabernacle & interment was made in the Gun Cemetery near town.
Source: The Robesonian, Lumberton, NC, Nov 16, 1914