"Don't Give It Up" was the third single and final single taken from British R&B singer Lemar's second album, Time to Grow (2004). Despite the song being remixed for single release, "Don't Give It Up" became Lemar's first song to miss the top 20 of the UK Singles Chart since the release of his debut, "Got Me Saying Ooh", in 2001. The song spent only four weeks within the UK top 75.
^"New Releases: Singles". Music Week. 30 July 2005. p. 37.