Achievements are now working again.
I issued an update a few days ago (~12MB) which meant achievements could be earned, but unfortunately this didn't appear to work for achievements which were already earned before that update. I've just now released another update (~33KB) which should perform a one-time re-grant of any achievements you've already earned.
Even if you've already uninstalled Sickness, the re-grant should still be possible, as long as you didn't remove all of the save/persistent data for this game from your computer.
The save/persistent directory can be found as follows:
Windows: %APPDATA%/RenPy/
OSX: ~/Library/RenPy/
Linux: ~/.renpy/
You probably wouldn't remove these files on your own without knowing it, but if you use cleaning or special uninstaller software on your computer, you might unknowingly remove it.
Anyway, it was the previous update which broke achievements in Sickness. Moving to a new build environment, with an updated version of the underlying engine, meant that not only was the last update huge, it was also missing the libraries this game uses to sync Steam achievements (they're optional additions, not something built-in). These have now been moved to the new build environment, and I certainly won't be making this mistake again. (Though hopefully no more fixes are needed for Sickness at this point regardless)