There is no evidence to suggest that it is the abbreviation of a longer phrase.
The saying and principle are traditional in the theatre, but they both originated in the 19th century with circuses.
If an animal got loose or a performer was injured, the ringmaster and the band tried to keep things going so that the crowd would not panic[1] because "it is a point of honour not to let the other players down by deserting them when no understudy is available".
[4] Eventually, the phrase was used to convey the idea that an event or activity must continue even if there are problems or difficulties, with or without regard to actual show business.
[5] This article about the English language is a stub.