The short answer here is No. You cannot map, nor logically find an object that has no unique properties or object hierarchy. It's not a flaw or bug. There is simply not enough information for TestComplete to recognize it as a unique object. It could guess...but then it would likely be wrong when the user enters different information. Likely why it's "shifting down" in your mapping because it thinks it's the same object.
I suggest using an image comparison or alternate method to check the page.
If you're attempting to click on one of these spans you may want to try clicking on the containing parent object and specifying coordinates. In this case you would click
<span class="twoLines displayGroup"> span object at X,Y coordinate (location of child span object).
If nothing else http://support.smartbear.com/viewarticle/55418/ TARGET='_blank'>Text Recognition may work for this.