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How big is your database?
I'm used to seeing this common php memory size error on sites using Drupal or Joomla, but not on the lightweight XOOPS sites.
The problem is your server ran out of memory for the script.
I'm assuming you have a fairly large database and it can't fit the info into memory. I tried this module out, but I tend to use phpMyAdmin and other methods to make backups of site databases.
You have a couple of solutions to get your database. First, you can ask your hosting company to increase the allowable size for scripts (in their server php config file). However, they may balk at this, as there really isn't much reason to need 20M of memory for a simple PHP script, and any web application using more than that is misbehaving IMHO (but Drupal and Joomla sites routinely need more memory than this). Alternatively, your hosting company might provide phpMyAdmin or some other way to do a dump of your database. If not, you could always install it on your site.