"Here's a little food for thought. It seems one big reason they wanted to redefine the kilogram was because the different prototype kilograms were diverging from each other, and they were a little puzzled as to why: was one losing mass or the other gaining mass, and so on. That and the research into using the Kibble balance meant they could move away from prototypes."
I certainly hope not; that would be a total fail on the part of scientists.
If they are diverging and they DO know why, then the redefinition has merit. Otherwise they're just bloody lazy and lack inquisitiveness.
No, as alluded to in the comment you're replying to, how do you investigate this? You need a mass reference to do it. Enter the Kibble balance. Now you have a way to measure mass that doesn't depend on a chunk of gold alloy. If it turns out to be something mundane like tiny amounts of wear or adsorption then you can watch it happening, but if the only way to measure mass is by comparing to another chunk of alloy which is also changing in some way then you're rather stuck.
Similar answer to the question of what happens if these universal constants aren't actually, you find some related processes that should be the same under your assumptions and start comparing them.