Event Registration fails with "We can't load the requested web page. This page requires cookies to be enabled..."

This is a difficult-to-reproduce error; I suspect there's an edge case somewhere that isn't being accounted for appropriately. I have been unable to trigger it myself, but I captured a few backtraces via watchdog. Here's one of them:

#0 public_html/sites/all/modules/civicrm/CRM/Core/Error.php(315): CRM_Core_Error::backtrace("backTrace", TRUE)
#1 public_html/sites/all/modules/civicrm/CRM/Core/Controller.php(278): CRM_Core_Error::fatal("We can't load the requested web page. This page requires cookies to be enable...")
#2 public_html/sites/all/modules/civicrm/CRM/Core/Controller.php(186): CRM_Core_Controller->key("CRM_Event_Controller_Registration", TRUE, FALSE)
#3 public_html/sites/all/modules/civicrm/CRM/Event/Controller/Registration.php(41): CRM_Core_Controller->__construct("Event Registration", "null")
#4 public_html/sites/all/modules/civicrm/CRM/Core/Invoke.php(287): CRM_Event_Controller_Registration->__construct("Event Registration", TRUE, "null", NULL, "false")
#5 public_html/sites/all/modules/civicrm/CRM/Core/Invoke.php(70): CRM_Core_Invoke::runItem((Array:15))
#6 public_html/sites/all/modules/civicrm/CRM/Core/Invoke.php(52): CRM_Core_Invoke::_invoke((Array:3))
#7 public_html/sites/all/modules/civicrm/drupal/civicrm.module(436): CRM_Core_Invoke::invoke((Array:3))
#8 [internal function](): civicrm_invoke("event", "register")
#9 public_html/includes/menu.inc(517): call_user_func_array("civicrm_invoke", (Array:2))
#10 public_html/index.php(21): menu_execute_active_handler()
#11