Taking a wild guess, I suspect you're running into invisible-to-the-eye jpeg compression artifacts. Even in blocks of apparently solid color you'll find inconsistencies, especially if the blocks (and your image) are not exact multiples of 8x8 pixels (jpeg's building block). This is especially true where you have sharp, high contrast edges. I suspect the problem independent of the conversion.
Point sample, as opposed to 3x3 or 5x5, can also give you inconsistent results, especially in photographic images, especially near high-contrast boundaries, and definitely if there is any noise in the image.
Try this experiment: set up a document with several blocks of solid color against a white background. Eyedropper around in the color blocks, especially away from the center, and note the readings. Now save the document as a jpeg, close and reopen. Repeat the eyedropper test.
Repeat the experiment, but this time use a document that's exactly 256 pixels square, and make the blocks of color exactly 80 pixels square, aligned on 8-pixel boundaries. See if you don't get a different result.
Mike Ninness gave an eye-opening (to me, anyway) session on image optimization at MAX last week, and the wild variation produced by jpeg compression was one of the major points. The "rule of 8" section starts at about 14m 40s.
[UPDATE AFTER Q CLARIFIED]
Increase your sample size in the eyedropper to a large enough value to smooth out the noise in the dithering. Dithering is necessary when changing profiles to maintain the visual relationships between different colors without banding (this is also why "Absolute Colorimetric" has to be avoided in normal use), but is (by definition) random. If you eyedropper too small a sample you'll get variations anywhere there's a color shift that can't be exactly replicated in the target profile.