Diagnosing plugin conflicts

Does your file-server have an error log in the WP Directory? I would start by turning on the DeBug and error reporting via the wp-config file. Open your wp-config and add this from the WordPress Codex Debugging page if it’s not already there:

    // Enable WP_DEBUG mode
    define('WP_DEBUG', true);

    // Enable Debug logging to the /wp-content/debug.log file
    define('WP_DEBUG_LOG', true);

    // Disable display of errors and warnings 
    define('WP_DEBUG_DISPLAY', false);
    @ini_set('display_errors',0);

    // Use dev versions of core JS and CSS file
    define('SCRIPT_DEBUG', true);

It should generate an error log and a debug log that may help locate the issue. It sounds like it takes a while for the issue to show up so disabling plugins one at a time might be a long solution. I’d start with the Maintenance Mode, and the BackWPup plugins and go from there.