THIS is one of my favourite Everlys tracks, first heard on their 1960 album A Date With the Everly Brothers and released as a single in 1961 as the B-side to Temptation.
It was written by Mel Tillis (1932-2017), a prolific songwriter whose biggest hit was probably Ruby, Don’t Take your Love to Town recorded by Kenny Rogers and the First Edition in 1969.
There is another version of Stick With Me Baby, recorded in 1960 and released in 1993 on the 2 CD set Walk Right Back – The Everly Brothers on Warner Bros 1960-1969. They definitely chose the right version in 1960.