Hello, does the skip not work at all, or does it skip a bit of text, and then stop again?
If it's the latter, then it's because you've unlocked a different branch of the story. While for some weeks, the general storyline stays the same, there are a lot of little branches depending on your previous choices and also your character's personality. So whenever you unlock a small branch, the skip will come to a halt.
The easiest way to check if your Skip function is working: you can set your Preferences to Skip All Text / Unread Text.
If it skips "properly" afterwards, then it's just as mentioned: before, you've unlocked unread branches of text so the skip also stopped there.