The Collaborative International Dictionary of English v.0.48:

Peter \Pet"er\ (p[=e]"t[~e]r), v. i. [imp. & p. p. Petered
   (p[=e]"t[~e]rd); p. pr. & vb. n. Petering.] [Etymol.
   uncertain.]
   To become depleted; to run out; to fail; -- used generally
   with out; as, that mine has petered out. [Slang, U.S.]
   [1913 Webster]