Hi Peter,
I think you are using a slitless Star Analyser, in which case I wonder if small tracking errors could be the cause. If the star moves or gradually drifts, then so would the spectrum and that would blur the final stacked spectrum. It does appear that the star at the zero order position just below 50 pixels in your first plot is located at a slightly different position between the stack and the single image.
Another check you can do is to compare the first and last image in the stack, or a selection of images in the stack.
I think there are several ways to align individual spectrum images before combining them in a final spectrum, either pre or post extracting the spectrum from the image, though I’ve never done this myself. That could potentially be used to fix tracking errors after the event. Though in general the better the tracking the better the results.
Cheers,
Andy