Had the same issue when adding a new product.
This time with messages:
Warning: getmypid() has been disabled for security reasons in Magento/app/code/core/Mage/CatalogIndex/Model/Catalog/Index/Flag.php on line 43
Warning: getmypid() has been disabled for security reasons in Magento/app/code/core/Mage/CatalogIndex/Model/Catalog/Index/Kill/Flag.php on line 27
Web host has disabled getmypid, which is used to get the thread’s process number from the server (as no two users can have the same process number at the same time). This is combined with the time to create a unique identifying string for temporary files.
Replaced it to rand(1,9999) and now import is working.