Is there any reason why you can't use the same sample for all your gravity readings rather than taking a fresh sample each time? The idea being to take an initial reading and then keep this sample separate from the main brew and use this sample purely for gravity checks.
I guess you're assuming the sample will continue to ferment with suspended yeast?
There's quite a few reasons why this can fail:
the sample may not be at the same temperature as the beer (both due to it's location plus it lacks the exothermic heat produced from the large volume of yeast in the main ferment.)
the sample may become contaminated and ferment with the help of contaminants (bacteria/wild yeast) resulting in a lower gravity than the main brew
the sample may not contain as much yeast as in the main brew, so ferments at a different rate
the sample may evaporate quicker (if uncovered and without an airlock)