Google and forum searches haven’t helped me with this one, although I did see a couple of very old reports (circa 2003 or so) of similar problems with no mention of the solution.
I created a mesh using front and side view background images in a split screen without incident. I decided to make a variation on the mesh, so I copied the .blend to a new directory, opened it up and loaded new background images. The image on the right becomes scaled to 0.25, and the size button will not increase it. I repeated this by trying to reload the original reference bitmaps (with new names), and again the image on the right shrank well out of proportion to its correct scale.
Further experiments showed that in some of the incremental saves I did when making the mesh, that I was able to load a new image for the right view and scale it correctly. I also note that this happens on two different machines. (Both Windows XP, Blender 2.45, both 4G). All reference images are PNGs, 1844x1844.
The later saved files would show an interesting variation: when I opened the background image dialog the existing background would warp to 0.25 without my using any further controls. The opening of the dialog was enough to resize the background.
I assume that I have inadvertently changed some setting in Blender which affects the background images, and that this setting persists in the saved .blend files. However I have not been able to find any clues on what this might be.
My short-term workaround was to export the mesh to .3ds, create a new scene and reimport the 3ds mesh. Background images resume their correct behavior.
I would appreciate learning what I did to cause this, and how to correct it in the future.