Missing save button and no autosave on field change

Looking at this code for the autosave functionality

      // There is only one editable field in that form, we can hide the submit
      // button.
      if ($this.find('input[type=text],input[type=checkbox],textarea,select').length == 1 || $this.find('input[type=radio] ').length > 1) {
        $this.find('.form-submit').hide();
        $this.find('input[type=text],input[type=checkbox],input[type=radio],textarea,select').change(function() {
          $this.find('.form-submit').triggerHandler('click');
        });
      }

This functionality should only happen if there is only one input, however I have seen cases where the save button disappears when there is a text field and a checkbox.

I am also having problems where the button is getting hidden but the click trigger is not working.
If I step through the code the trigger line is getting run but nothing happens.

I don't have time to investigate further right now but hope to dig a bit deeper soon.
The site in question is a bit of a mess so it is possible that some other custom code is affecting things.