This is a known bug with the platform and the solution is not pretty.
What is happening is that at the start of the first game on a given day, everyone who played the day before and is playing in one of the first slew of games loses their stats. My solution right now (short-term) is to re-run stats daily for the last few days, so that's why stats disappear and then re-appear. I have a more permanent solution, but it involves rewriting the entire stats engine. This would be good to save for the offseason I think.
Let me know if this makes sense. Oh, and why do those players lose stats at that time every day? That... that I cannot answer. Believe me when I tell you I'm very, very familiar with that portion of the code right now. Looking there is a big reason why I didn't make that lineups page fix earlier.