A change of the "Image quality" for an embedded/linked image can't be saved in some circumstances.

Inkscape 0.91 r13725 x64 (MSI)
Windows 7 SP1 x64

Steps to reproduce the problem: (You can skip steps #1-#6 if you already have a file with a PNG/JPG type image saved in it.)
1. Start with a fresh profile. (this isn't really necessary, as I can duplicate it with my normal profile, but as a safety net)
2. Find an image you want to import into Inkscape via Windows Explorer.
3. Now, right click on the image > Open with > Inkscape.
4. When the 'import' screen shows up, Select the following options: 'Link' ; 'From file' ; 'None (auto)'
5. Once the Inkscape window loads with the image you selected, save it as an SVG file (doesn't matter where).
6. Once the SVG is saved, open the SVG file in a text editor (keep Inkscape open, but minimized) and notice that there is no 'style' info for the image.
7. Now, go back into Inkscape and right click on the image and then go into 'Object Properties'.
8. Now, go to the 'Image Rendering' and change it to either of the other two options (doesn't matter as long as you don't leave it on 'auto' or whatever setting it was already set as).
9. Hit the 'Set' button to lock in the change.
10. Try to save the image again.

What happens:
Inkscape refuses to resave the image. It thinks nothing was changed, even though you did change how the image was suppose to be rendered.

What should happen:
Inkscape should save the SVG file without objecting since you did change something in it.

Work around(s):
1. File > Save As --- that allows the change in the 'Image Rendering' to be saved into your SVG file.
2. Do something else in the file that is registered as a 'change'.

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This also happens if the image is already saved on a layer. So, the '(root)' layer isn't the cause here.