In the UK, where the Gladys Knight & the Pips original of "Giving Up" failed to chart in its June 1964 release, a belated cover of the song was recorded in 1965 by Julie Grant with her regular producer Tony Hatch and released that March without evident result. Bill Kenwright also had a UK single release of "Giving Up" in August 1968, the track being the B-side of the non-charting single "Love's Black and White".
The song's composer Van McCoy produced a 1969 cover of the song by the Ad Libs that peaked at No. 34 on the US R&B chart.
Donny Hathaway remade "Giving Up" for his 1971 self-titled album for which it served as lead single reaching No. 21 R&B in the summer of 1972. Hathaway's version crossed over to the pop chart, peaking at No. 81 on the Billboard Hot 100. sax player Kirk Whalum recorded "Giving Up" for his 2010 tribute album Everything Is Everything: The Music of Donny Hathaway.