I threw this all in one controller for testing purposes.
My code fills out the form correctly for adding a new address to your Amazon account. There are two buttons that submit this form, one takes you to add a new address which is what I don't want, and the other is just a Save & Continue input/image. 
When I submit the form via that button, as I do below, the form is still on the page, filled out as I have with my code. Inspecting the page titles, they're the same. There are no discernible errors that Mechanize or Amazon spit back.
Any ideas?
class AmazonCrawler
  def initialize
    @agent = Mechanize.new do |agent|
      agent.user_agent_alias = 'Mac Safari'
      agent.follow_meta_refresh = true
      agent.redirect_ok = true
    end
  end
  def login
    # login_url = "https://www.amazon.com/ap/signin?_encoding=UTF8&openid.assoc_handle=usflex&openid.claimed_id=http%3A%2F%2Fspecs.openid.net%2Fauth%2F2.0%2Fidentifier_select&openid.identity=http%3A%2F%2Fspecs.openid.net%2Fauth%2F2.0%2Fidentifier_select&openid.mode=checkid_setup&openid.ns=http%3A%2F%2Fspecs.openid.net%2Fauth%2F2.0&openid.ns.pape=http%3A%2F%2Fspecs.openid.net%2Fextensions%2Fpape%2F1.0&openid.pape.max_auth_age=0&openid.return_to=https%3A%2F%2Fwww.amazon.com%2Fgp%2Fcss%2Fhomepage.html%3Fie%3DUTF8%26ref_%3Dgno_yam_ya"
    login_url = "https://www.amazon.com/gp/css/account/address/view.html?ie=UTF8&ref_=ya_add_address&viewID=newAddress"
    @agent.get(login_url)
    form = @agent.page.forms.first
    form.email = "
[email protected]"
    form.radiobuttons.first.value = "0"
    form.radiobuttons.last.check
    form.password = "my_password"
    dashboard = @agent.submit(form)
  end
end
class UsersController < ApplicationController
  def index
    response = AmazonCrawler.new.login
    form = response.forms[1]
    # fill out form
    form.enterAddressFullName == "Your Name"
    form.enterAddressAddressLine1 = "123 Main Street"
    form.enterAddressAddressLine2 = "Apartment 34"
    form.enterAddressCity = "San Francisco"
    form.enterAddressStateOrRegion = "CA"
    form.enterAddressPostalCode = "94101"
    form.enterAddressPhoneNumber = "415-555-1212"
    form.AddressType = "RES"
    new_response = form.submit( form.button_with(value: /Save.*Continue/) )
  end
end