I would check the permissions on your var directory. It could be that the cache cannot be written because it is failing on permissions.
To check this, look in the /var/yoursite/cache/ folder and see how many files are in there. Remove them and see if they are rewritten next time you load a page. Or debug output should tell you as well.
Also, if you run the 'bin/php/makestaticcache.php' with debug and verbose flags you will get a warning if you can't find the pages to generate the static cache from. After you have run this script successfully ther shuold be files and directories in your /static-folder.
The setting permissions did the trick. One thing is that when I ran the makestaticcaches.php script with debug on, I get the following message.
#################################### DEBUG ####################################
Notice: (eZMySQLDB::query(0.000 ms) query number per page:0) SET NAMES 'latin1'
Notice: (Static Cache) Could not grab content, is the hostname correct and Apache running?
Fiddle a little with settings in 'staticcache.ini' especially HostName. For me the wrong url was accessed.
To see what url is accessed when the makestaticcaches.php script is run i did a little hack modifing one of the kernel files...
# diff ezpublish-3.7.3/kernel/classes/ezstaticcache.php public_html/kernel/classes/ezstaticcache.php
333c333
< eZDebug::writeNotice( 'Could not grab content, is the hostname correct and Apache running?', 'Static Cache' );
--- > eZDebug::writeNotice( $fileName . ': Could not grab content, is the hostname correct and Apache running?', 'Static Cache' );
This allows me to see what really was accessed but of course you should never alter the kernel code as these changes will be overwritten if you upgrade...