babel: _regeneratorRuntime is not defined when using JSON.stringify (T7041)

Issue originally made by @neverfox

Bug information

• Babel version: 6.4.5
• Node version: 5.3.0
• npm version: 3.5.2

Options

{
  "presets": ["es2015", "react", "stage-0"],
  "plugins": ["transform-runtime", "add-module-exports", "transform-decorators-legacy"]
}

Input code

import fetch from 'isomorphic-fetch'

function checkStatus (response) {
  if (response.status >= 200 && response.status < 300) {
    return response
  } else {
    var error = new Error(response.statusText)
    error.response = response
    throw error
  }
}

function parseJSON (response) {
  return response.json()
}

function authorizeApi ({ username, password }) {
  return fetch('http://localhost:3001/auth', {
    method  : 'POST',
    headers : {
      'Content-Type' : 'application/json'
    },
    body : JSON.stringify({
      type  : 'basic',
      value : btoa(`${username}:${password}`)
    })
  })
  .then(checkStatus)
  .then(parseJSON)
}

export function * authSaga () {
  yield authorizeApi({ username: 'username', password: 'password' })
} 

Description

I have a working code module using generator functions, but when I add a use of JSON.stringify anywhere in the same file, I start getting the _regeneratorRuntime is not defined error that you get when generators aren’t recognized. Adding babel-polyfill makes no difference.