Douglas Harper's Etymology Dictionary
go south
"vanish, abscond," 1920s, American English, probably from mid-19c. notion of disappearing south to Mexico or Texas to escape pursuit or responsibility, reinforced by Native American belief (attested in colonial writing mid-18c.) that the soul journeys south after death.
Wiktionary
go south
vb. (context idiomatic English) To become unfavorable; to decrease; to take a turn for the worse.
Usage examples of "go south".
When things started to go south for Apple, they should have ported their OS to cheap PC hardware.