Losing religion is a metaphor or euphemism for cursing used in some rural areas of America.
The phrase is based on the scriptural proscription of curses, that is, calling upon the Almighty to visit eternal damnation upon something.
A related phrase "we lost of a lot of religion" used to describe an activity that went poorly and resulted in a loss of temper and cursing; often said of performing repairs on equipment.
The rock band R.E.M.'s song "Losing My Religion" is loosely based on this phrase. In an interview with Michael Stipe, he states that: "... In the South, in Georgia, where we live, if you say that you're 'Losing your religion' basically means that you're at the end of your rope, or that you've had it, you're fed up".
References
Losing religion Wikipedia(Text) CC BY-SA