The phrase “to keep the pot boiling” means: To provide for one’s living; to keep at gainful employment that will produce income; also, to keep interest from flagging; to keep the ball rolling.
In former times when gentlemen and ladies were not supposed to work, to sell their time and effort for wages, some still found it necessary to produce some sort of salable commodity in order to continue to eat.
It was genteel, not vulgar labor, to write or to paint, and many a man in the early nineteenth century especially (and from then to the present time) kept food in his domestic pot and a fire under it, through the judicious exercise of these talents and the generosity of a benefactor.
Thus we find William Combe, himself a “potboiler” through long practice, in The Tour of Doctor Syntax in Search of the Picturesque (1812), saying in his customary doggerel: “No fav’vring patrons have I got, But just enough to boil the pot.”
