petered out
Declined slowly to almost nothing. American slang.
To me the first note of warning came from an American gentleman, who told me that the same thing had been a great "boom" in the States, but that it had "petered out" and was not now believed except in very unsophisticated country places.
The "Georgia Magnet": A Statce to Mr. H. W. Schneider at Barrow. The Manchester Guardian. November 23, 1891. Page 8. Viewed in ProQuest Historical Newspapers.