Hey there,
Since I've started the third day I'm no longer receiving a skill point when leveling up. I leveled up four times already without getting a skill point. Not sure what's causing this. Did this happen to anyone else? Could this be a bug?

Just have the same problem here. It begin in the 2nd day of the game for me.

I know this is almost a year old but for anyone who has this bug, my solution was to access the save file data located :

C:\Users\(your user name)\AppData\LocalLow\ZAUM Studio\Disco Elysium\SaveGames

find the save that is bugged, extract it. Find the file ending in ".2nd.ntwtf.json"

open with notepad and scroll down till you find

"PlayerCharacter" section (nearish top after all the skill types)

" skills " value ( mine was at -5 lol) and change it to how many you think you should have save then re-compress it and put it back. (make sure you have a back up of course) make sure you re-compress the files not the folder. (and same name as before)

Hope this might help someone in the future.