1
general::
Dwindle or diminish and come to an end, as in Their enthusiasm soon petered out. The origin of this usage is unknown, but one authority suggests it may refer to the apostle Peter, whose enthusiastic support of Jesus quickly diminished so that he denied knowing him three times during the night after Jesus's arrest. [Mid-1800s]
American Heritage Idioms
2
general::
Phrase(s): peter out
[for something] to die or dwindle away; [for something] to become exhausted gradually. • When the fire petered out, I went to bed. • My money finally petered out, and I had to come home.
McGrawhill's American Idioms And Phrasal Verbs