Error: Unsupported product type “type”

Question

Using Magento EE 1.13.0.1 when saving or duplicating some products (but not all) we get the error:

Unsupported product type "type".

Stack trace:

exception 'Mage_Core_Exception' with message 'Unsupported product type "type".' in /var/www/magento/app/Mage.php:595
Stack trace:
#0 /var/www/magento/app/code/core/Enterprise/Catalog/Model/Index/Action/Product/Price/Abstract.php(290): Mage::throwException('Unsupported pro...')
#1 /var/www/magento/app/code/core/Enterprise/Catalog/Model/Index/Action/Product/Price/Refresh/Changelog.php(82): Enterprise_Catalog_Model_Index_Action_Produ$
#2 /var/www/magento/app/code/core/Enterprise/Catalog/Model/Index/Action/Product/Price/Refresh/Changelog.php(50): Enterprise_Catalog_Model_Index_Action_Produ$
#3 /var/www/magento/app/code/core/Enterprise/Mview/Model/Client.php(109): Enterprise_Catalog_Model_Index_Action_Product_Price_Refresh_Changelog->execute()
#4 /var/www/magento/app/code/core/Enterprise/Catalog/Model/Index/Observer/Price.php(114): Enterprise_Mview_Model_Client->execute('enterprise_cata...')
#5 /var/www/magento/app/code/core/Mage/Core/Model/App.php(1338): Enterprise_Catalog_Model_Index_Observer_Price->processCatalogPriceRulesApplyEvent(Object(Va$
#6 /var/www/magento/app/code/core/Mage/Core/Model/App.php(1317): Mage_Core_Model_App->_callObserverMethod(Object(Enterprise_Catalog_Model_Index_Observer_Pri$
#7 /var/www/magento/app/code/core/Mage/CatalogRule/Model/Action/Index/Refresh.php(644): Mage_Core_Model_App->dispatchEvent('catalogrule_aft...', Array)
#8 /var/www/magento/app/code/core/Mage/CatalogRule/Model/Action/Index/Refresh.php(131): Mage_CatalogRule_Model_Action_Index_Refresh->_prepareAffectedProduct$
#9 /var/www/magento/app/code/core/Mage/CatalogRule/Model/Resource/Rule.php(592): Mage_CatalogRule_Model_Action_Index_Refresh->execute()
#10 /var/www/magento/app/code/core/Mage/CatalogRule/Model/Resource/Rule.php(545): Mage_CatalogRule_Model_Resource_Rule->_reindexCatalogRule(Object(Mage_Cata$
#11 /var/www/magento/app/code/core/Mage/CatalogRule/Model/Rule.php(349): Mage_CatalogRule_Model_Resource_Rule->applyAllRules(Object(Mage_Catalog_Model_Produ$
#12 /var/www/magento/app/code/core/Mage/CatalogRule/Model/Observer.php(53): Mage_CatalogRule_Model_Rule->applyAllRulesToProduct(Object(Mage_Catalog_Model_Pr$
#13 /var/www/magento/app/code/core/Mage/Core/Model/App.php(1338): Mage_CatalogRule_Model_Observer->applyAllRulesOnProduct(Object(Varien_Event_Observer))
#14 /var/www/magento/app/code/core/Mage/Core/Model/App.php(1317): Mage_Core_Model_App->_callObserverMethod(Object(Mage_CatalogRule_Model_Observer), 'applyAl$
#15 /var/www/magento/app/Mage.php(448): Mage_Core_Model_App->dispatchEvent('catalog_product...', Array)
#16 /var/www/magento/app/code/core/Mage/Core/Model/Abstract.php(344): Mage::dispatchEvent('catalog_product...', Array)
#17 [internal function]: Mage_Core_Model_Abstract->afterCommitCallback()
#18 /var/www/magento/app/code/core/Mage/Core/Model/Resource/Abstract.php(110): call_user_func(Array)
#19 /var/www/magento/app/code/core/Mage/Core/Model/Abstract.php(322): Mage_Core_Model_Resource_Abstract->commit()
#20 /var/www/magento/app/code/core/Mage/Catalog/Model/Product.php(1143): Mage_Core_Model_Abstract->save()
#21 /var/www/magento/app/code/core/Mage/Adminhtml/controllers/Catalog/ProductController.php(792): Mage_Catalog_Model_Product->duplicate()
#22 /var/www/magento/app/code/core/Mage/Core/Controller/Varien/Action.php(418): Mage_Adminhtml_Catalog_ProductController->duplicateAction()
#23 /var/www/magento/app/code/core/Mage/Core/Controller/Varien/Router/Standard.php(250): Mage_Core_Controller_Varien_Action->dispatch('duplicate')
#24 /var/www/magento/app/code/core/Mage/Core/Controller/Varien/Front.php(172): Mage_Core_Controller_Varien_Router_Standard->match(Object(Mage_Core_Controlle$
#25 /var/www/magento/app/code/core/Mage/Core/Model/App.php(354): Mage_Core_Controller_Varien_Front->dispatch()
#26 /var/www/magento/app/Mage.php(684): Mage_Core_Model_App->run(Array)
#27 /var/www/magento/index.php(87): Mage::run('default', 'store')
#28 {main}

And the product's entry in catalog_product_entity with type_id set to "Simple"

# entity_id, entity_type_id, attribute_set_id, type_id, sku, created_at, updated_at, has_options, required_options
'10234', '10', '64', 'simple', 'ROK11058', '2014-05-30 13:00:12', '2014-06-09 00:21:57', '0', '0'

Has anyone seen this before? We're not sure what makes this product special, or why it's doing this.