"Course, I never was great shakes at magic, really... but at least he never saw me expelled. Died, see, in me second year..."
-- Hagrid (GF24)
His mother having abandoned them years earlier, Hagrid is essentially orphaned upon his father’s death (GF23).
All we know is that Hagrid's father died during his second year (GF24), so it's equally possible that his death was between September 1941 and June 1942. Since there are more of those months in 1942, we're placing it in that year.