ah, ok, I see. This is very likely related to a change in the default configuration of PHP 5.3, due to which saving large tables can cause trouble. Due to the large number of text fields and checkboxes, PHP will not let the request get through, and basically reset the checkboxes.
Instead of bothering with an ugly fix, I suggest that you switch to the TablePress plugin, which I'm currently working on. TablePress is (or rather will shortly be) the official and designated successor of WP-Table Reloaded, where this problem does no longer occur, as the plugin uses a different saving mechanism. You can get TablePress at http://wordpress.org/extend/plugins/tablepress/ . The migration from WP-Table Reloaded to TablePress is very easy, and more information can be found at http://tablepress.org/migration-from-wp-table-reloaded/ .
In your case, you will then also need to update the Filtering Extension with this version: http://tablepress.org/extensions/row-filter/