Without being too specific re the 1911 census, there were two Sarah E's in Sheffield, one aged 40 (yours) and one aged 41.
As well as the Gainsborough death, there was this one in Sheffield
Deaths Jun 1954
Downing Sarah E 86 Sheffield 2d 143
One of Sarah's children (Grace Jane, 1902) may well have died unmarried in Sheffield in 1946, so perhaps the family were still there at that time.