\version "2.18.2"

% this code is the second example at http://lilypond.org/doc/v2.18/Documentation/notation/modifying-single-staves#ossia-staves ; only the \breathe was added to demonstrate the problem
\new Staff = "main" \relative c'' {
  c4 b d c \breathe
  <<
    { c4 b d c }

    \new Staff \with {
      \remove "Time_signature_engraver"
      alignAboveContext = #"main"
      fontSize = #-3
      \override StaffSymbol.staff-space = #(magstep -3)
      \override StaffSymbol.thickness = #(magstep -3)
      firstClef = ##f
    }
    { e4 d f e }
  >>
  c4 b c2
}