It sounds like your hitting some sort of server resource limit, likely max_execution or memory_limit, could you check your php error logs?
[15-Jul-2012 14:11:42] PHP Fatal error: Call to undefined function hmbkp_in_progress() in /home/public_html/wp-content/plugins/backupwordpress/admin.backups-table.php on line 4
[15-Jul-2012 14:11:51] PHP Fatal error: Call to undefined function add_action() in /home/public_html/wp-content/plugins/backupwordpress/admin.menus.php on line 12
[15-Jul-2012 14:12:32] PHP Fatal error: Call to undefined function hmbkp_in_progress() in /home/public_html/wp-content/plugins/backupwordpress/admin.page.php on line 1
[15-Jul-2012 14:12:40] PHP Fatal error: Call to undefined function hmbkp_get_disable_automatic_backup() in /home/public_html/wp-content/plugins/backupwordpress/admin.status.php on line 7
[15-Jul-2012 14:12:49] PHP Fatal error: Call to undefined function get_bloginfo() in /home/public_html/wp-content/plugins/backupwordpress/plugin.php on line 52
[15-Jul-2012 14:12:58] PHP Fatal error: Call to undefined function __() in /home/public_html/wp-content/plugins/backupwordpress/admin.constants.php on line 3
[15-Jul-2012 14:13:09] PHP Fatal error: Call to undefined function add_action() in /home/public_html/wp-content/plugins/backupwordpress/admin.actions.php on line 105
[15-Jul-2012 14:14:13] PHP Fatal error: Call to undefined function hmbkp_in_progress() in /home/public_html/wp-content/plugins/backupwordpress/admin.backup-button.php on line 1
[15-Jul-2012 14:14:22] PHP Fatal error: Call to undefined function hmbkp_get_backups() in /home/public_html/wp-content/plugins/backupwordpress/admin.settings.php on line 1
I don’t what those errors are, most of those are standard WordPress functions.
Did you try to load the plugins files directly?