Wendy is right, Pam, and most people - group administrators included - do not understand this. I submitted one to a group by mistake after an administrator had informed us that s/he was going to be on vacation and would not accept new submissions until s/he returned. S/he rejected all images submitted during that time - as promised. I just went to the image in question, opened edit, scrolled down to the Groups box, unchecked the box, and submitted. Then I went in again, scrolled down, and checked the box. It was featured today so obviously this worked.
I simply do not submit more than one at a time, regardless of the group policies. And I submit from the Group's page, not from my image edit page so it's no problem to remember. I do essentially what Lee does and pick a time when I can go from group to group, submitting an image to each as long as I don't have one pending.
I think features count for something, simply having an image accepted into a group does not. If you submit five at a time, chances are only one (if any!) will be featured. But if you submit the same five images spread out over, say two weeks, your chances of having several of them featured (provided they are a good fit for the group and excellent images) are excellent. I belong to many groups, but I only have a limited number of images that are appropriate for any of them. Why would I want to put them all in at once and then have nothing left to submit a week or a month later?