Sorry for not replying earlier.
The problem with HTML image maps is that they use only absolute values for coordinates. If the size of the image is different the values will not match.
This is however fixed in ImageMapster, the jQuery plugin the ImageMapper uses. When images are resized, the browser will detect the change and calculate new values for every image area. Responsive Image Maps does the same.
However it seems that sometimes the change is not detected correctly. As I'm not the developer of ImageMapster nor Responsive Image Maps it's hard to me to say where's the problem.
There's also another problem which may cause the bugs in image maps. The image map of ImageMapster consists of two images, an HTML5 canvas element and an HTML image map. Only one of the images are actually used to display the image. Canvas is used to draw highlights and other effects and the other image is a transparent layer which handles the mouse functionality with HTML image map set to it. The problem is that some WordPress themes resize the display image without resizing the canvas and the transparent image. All of the layers' sizes have to be equal or the image maps won't function properly.
I hope this helps.