Does this happen in a new game, or in old saves where the skills were working properly?
If so, for the Steam version, did you try verifying local files? In the Steam library, right click on Divinity Original Sin and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Cache...' button.
For GOG you can try a clean re-install (uninstall, reboot, make sure there is nothing left in the install folder, shut down all non-essential programs, re-install the game and patch).

You could also try browsing to the '..\Documents\Larian Studios' folder and renaming the 'Divinity Original Sin' subfolder.
This folder contains the saved games, configuration files and a level cache folder. Deleting or renaming it will get the game to recreate it on startup; playing the game from a different Windows user account would effectively do the same thing.
After that, start D:OS, create a new profile and exit. Copy a save from your renamed folder to the newly created profile's savegames folder, or start a new game, to check the skills.
If that helps, move the rest of your saves from the previous folder to the new profile(s); if not, delete the new D:OS folder and rename the original back again.

If neither help, the problem may be in the saves. In that case, please email supportdos@larian.com, with a description of the problem and the report.zip file generated by the D:OS support tool (for the PC version). The report will contain system and game information, any crash dumps, and your saved games. If file size is an issue, you can delete many of the saves, leaving a few representative examples.