You know that one that is supposed to play when you start up Fo4... mine hasn't shown in over a month now and I don't know why it has stopped being played

I really liked seeing it. Guess I'm not the only one haha, any fixes though?

I know what you mean. I think I encountered one of the shorts once in the past week but I accidentally skipped it.

Whether or not an episode plays is decided by a Random Number Generator. First, roll to see Yes/No. If Yes, then roll again to see which of the 7 episodes plays. I'm fairly certain that early on Yes had a plus die modifier. After X number of gameplay hours, the modifier gets dropped and you start to experience the rare showings.

[My wife experienced the same thing as you, not seeing any SPECIALs for about a month. Then they started to appear again, about once-in-three game starts.]

You can see these videos on Bethesda's Youtube channel.