the customer resource model does not allow you to modify is_active field,
you can either run a raw sql or add is_active field in default attributes array in Mage_Customer_Model_Entity_Customer::_getDefaultAttributes()
$log_customer = Mage::getSingleton('customer/session')->getCustomer(); Mage::registrer('isSecureArea', true);//you can delete a customer from the admin only. This emulates the admin - sort of $log_customer->delete(); Mage::unregister('isSecureArea');//reset admin emulation
This code will actually delete the customer from your database.