The only time I ever remove shrink is if the item can easily slip out of it without tearing more shrink. Otherwise I leave it on and bag the items to prevent further damage. I personally never re-shrink(don't own a machine) as buyers will probably avoid buying once they think you are re-shrinking.

Personal decision this. Me, I tear off that old stinky plastic. That way you can appreciate the item (open it and read it) ... you are not here forever, worth having a look at stuff.  

The reason that shrink wrap existed was to cheaply protect the module (or box etc.) from wear and hold the contents inside. If your ratty shrink wrap is doing none of the above, why keep it? Because the valuation will go down the moment that ratty shrink wrap is removed, people will say. Well then, haven't we arrived at the crux of the issue, that shrink aficionados have so driven up the price for items that the presence of cheap shrink wrap so dramatically effects the sale price. It is Orwellian that items in shrink wrap are (currently) selling for 3x (or more) what items not in shrink wrap sell for, in many cases regardless of the actual condition of the item. The actual value of (original) shrink wrap is that one can easily tell that an item is complete and has not been written in. The down side is that items in shrink wrap are unable to be checked for staple rust and bending (if they are inside boxes). While I expect prices to keep rising on TSR collectables, I think (hope?) that the shrink curve will flatten out (pun intended), items will be judged on quality of their condition, not the presence of shrink wrap, but until that day comes NMilty, from a financial perspective, leave the ratty shrink on and toss it in a polybag.

stratochamp wrote in Should I Reshrink??:... leave the ratty shrink on and toss it in a polybag.

I would sometimes get items that greatly exaggerated their condition while still in shrink.  After giving the person a rough rating on eBay, I too would sometimes bag it and mentally cross the seller off my reputable list.  When 30%+ of the shrink wrap is off, it serves no useful function at that point.

- SKA