I would sell immediately.
Lower ratings - the entertainment market is so big and segmented. People can get HBO Go, Hulu, Netflix, Amazon Prime, ect. People have a lot of options of what they can watch these days.
If people want to see men (or women) in a violent sport, they can watch UFC or other MMA promotion.
Players getting brain damage. Will they have to change the game and make it less violent? Fans won't go for that. Will top players retire sooner out of fear of damage? Will top athletes continue to play the sport as kids? Around my area the sport participation rates is declining.
Players breaking laws and getting caught. A player this week is being accused of beating his wife. It seems so common that it isn't that big of a story.
Players protesting. I do not watch the NFL so I don't care about the protests but I could see people getting annoyed that millionaires are protesting against oppression. People go to the games to be entertained. They don't want to get into politics. Sure some agree with the protest. But what happens if another player protests against abortion. Another one protests against limits to the 2nd Amendment. Another protests against the Affordable Care Act ect.
I only see the viewership in decline.
To be honest, I thought the same about baseball for the past number of years. It seemed to me there isn't a younger audience that is going to be as big as fans as the older crowd today. But I have been wrong about that one for years.
I don't see the NFL going bankrupt any time soon. But I think its best days are behind them.