Back on topic, if I may...
Here's a PFT article discussing the possible reasons for the downturn. Unfortunately, I really don't believe it has anything to do with Framegate at all. After all, why wouldn't the ratings have fallen off last year (that's when I stopped watching or caring)? Sure, Brady got out of the suspension (temporarily), but that didn't really change the NFL's actions. They still did all that lying, framing, and over-punishing, it was a federal judge who tried to restore some fairness to the situation.
Judging by the number of people who tune in to the Olympics each year it's on, I'm going with the national anthem protests. A lot of people will tune in to almost any crap on TV, so long as it promotes the USA. Mess with that at your peril.
Why is TV viewership down?