Currently, I can't skip any dialogues. It didn't even show prompt during dialogue like before. At first, I thought that it is a side quest bug, but now I see that it is not working at all.
I repair files, but it seems that my save file is corrupted somehow.

Also, I think it can be related to one situation when I went out of the shop during dialogue, it seems that after that my problem started...

My previous save where skipping is working is from 6 hours ago, so it makes no sense for me to go back to this save.

I didn't change bindings, so it was always C default.

There are another couple of threads about the same thing here on the forums (can't post link). Seems there's a bunch of us with this issue. No fix yet. I'd suggest opening the support ticket.

@nadarath in another thread found the cause of this for him and at least two more people including myself. I can't post a link because the forum blocks link posting but I will quote his post:

"I had this bug for around 20-30 hours of game time and I just got rid of it.
I have some vague idea of what might be wrong.

I did all the Evelyn and Panam quests then I've stoped doing main story quests and got left with Gimme Danger - the part where you need to talk to Takemura near to stalls. And I remember runing past him - triggering his dialogue but I never did follow up on his quest. Once I was done with all the side quests I could do I came back to Gimme Danger quest. Once I've progressed a bit and got to talk to Takemura near food stand the Skip Dialogue option was back.

So either this is related to triggering some quest and not doing it. Or i just got lucky. Maybe it will help someone with similar problems."