How can I fix my server so core/plugins/theme update don’t silently fail?

There is a bug in some versions of PHP itself, unzip hangs.
PHP 5.2.17 hangs,
PHP 5.3.24 works as expected.

PHP Change Log http://www.php.net/ChangeLog-5.php#5.3.4 says
PHP Version 5.3.4 released 09-Dec-2010 – “Fixed crash in zip extract method (possible CWE-170)”. (Note: 5.3.24 released 11-April-2013, and is no longer the latest version.)

http://lcblog.lernerconsult.com/2013-php-unzip-bug-makes-wordpress-updates-hang/ has the PHP program I used to demonstrate the bug is PHP not WordPress or plugins.