Separate permissions for form access and form submit
It's an odd use-case where certain roles can view the form itself, but not submit it. Perhaps better to allow non-privileged users to view the rendered form output instead of the input form.

That way, you can put the access check on the menu callback for the form itself.

Anyway, have you considered putting the access check into the form validate function?

e.g

function members_edit_form_validate($form, &amp;$form_state)
{
  if (!user_access('low admin tasks'))
  {
    form_set_error('submit', t('Sorry, you do not have access to update this form'));
  }
}