In another thread, I noticed the use of petered out.
The earliest example of “petered out” I could find was in a poem by Bret Harte, called DOW’S FLAT, published in 1856:
Then the bar petered out,
And the boys wouldn’t stay;
And the chills got about,
And his wife fell away;
But Dow in his well kept a peggin’ in his usual ridikilous way.
I did manage to find some interesting speculation on the etymology of the term:
From The Dial, Vol. 45, November 1, 1908, pp. 284, 285:
[Edited to add better links]