How to keep HTML form field that is conditional hidden with javasript hidden after page reload?

Try this code:

// Conditionally show price
(function ($) {
  window.onload = function() {

  if ($("#select_price_option").val() == "I need more information") {
   $('#price_input_div').hide();
  }

$("#select_price_option").change(function() {
  if ($(this).val() == "I need more information") {
    $('#price_input_div').hide();
  } else {
    $('#price_input_div').show();
  }
 });
 }})(jQuery);