The reason is when you installed SUPEE 7405, it modified all permission within the site to be able to prevent some security breach.
This was known issue, and now magento has issued a new patch:
You will need to install one more patch to your site.
Today, we are distributing updates that improve our most recent
security release. SUPEE-7405 v1.1, Enterprise Edition 22.214.171.124, and
Community Edition 126.96.36.199 add support for PHP 5.3 and address issues
with upload file permissions, merging carts, and SOAP APIs experienced
with the original release. They DO NOT address any new security
NOTE: SUPEE-7405 v1.1 is a patch of a patch and therefore v1.0 is a prerequisite before installing v1.1. From the release:
You must install the SUPEE-7405 v 1.0 patch before installing the
SUPEE-7405 v 1.1 patch bundle if you are running a version of Magento
Enterprise Edition prior to 188.8.131.52 or Magento Community Edition
prior to 184.108.40.206
You can also check this