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.