You have to enable zlib compression in php.ini

zlib.output_compression = On
With Ubuntu :

sudo nano /etc/php5/apache2/php.ini

Next/previous page to move > move the cursor with the arrows > modify (zlib.output_compression = Off > zlib.output_compression = On) > Ctrl + o > Ctrl + x

sudo service apache2 restart
Then, go in Phpmyadmin > clear session table.

It should work again.

A session id has not been properly registered on the server and in the database.

Check cron jobs in vbulletin (update of hit counter, schedulde tasks, ...).