Simple past tense and past participle of peter out.
Wiktionary
Petered-out Sentence Examples
This rain spread into the Midlands and East Anglia during the morning, then gradually petered out.
However, the passage eventually petered out in a narrow rift.
The investigation had finally petered out with no results.
The rising was never finally crushed; it simply petered out.
The flannel suits quickly gained popularity among men, too, and in fact were worn by men well into the twentieth century, while the usage by women had soon petered out.
