I checked this error and a similar instnce happened in the following Moodle article.
They say "getting the included libzip up to the latest version (0.10.1) might help with this and certain other issues (currenly PHP is complied with 0.9.1)." This article was getting a different error than yours though. They were restoreing a large backup .zip file to their moodle.
It seems if it was working prior to the upgrade, then you will want to check your PHP module versions to make sure they are up to date. Its possible the old server configuration worked well with the older Moodle but when you upgraded the newer version of Moodle requires a new PHP module Unfortunately, which module it could be is unkown.
You will want to check the apache and logs to see the error when it happens. To check the apache logs on teh fly you can do the following thruogh shell.
tail -f /usr/local/apache/logs/error_log | grep domain.com
This will pause the log and display any errors when the error occurs. Run that command and then replicate teh error in your Moodle site to see if any apache errors are thrown.
To get your PHP logs, you will have to enable PHP error logging. To enable error login you will need to follow the steps in teh following article.
Display and log errors for PHP
If you can get the server to display an error in Apache or PHP then you will be able to pinpoint the exact failure. Hope this gets you in the right direction.