Since the 2011 season, the Pats have been down 21 points exactly 6 times. The Pats managed to win 3 of these games, and had a significant chance in two of the other three games (tied one game with 6 minutes remaining, and had the ball while down 7 with a minute left in another). The sixth game is the infamous 2014 KC game where Brady's starting job was questioned, it was determined "the New England Patriots, let's face it, they're not good anymore", but we were on to Cincinnati.

• 2011 week 17 Bills @ Pats (Pats down 0-21 in first quarter; win 49-21),
• 2012 week 15 49ers @ Pats . Pats down 3-31 with 10:31 left in 3Q, manage to tie game at 6:43 4th quarter, but lose 41-34.
• 2013 Broncos @ Patriots week 12. Pats down 0-24 at half, win 34-31 in OT.
• 2014 Patriots @ Chiefs week 4. Pats 41-7 and didn't make a comeback (lose 41-14 with Brady pulled).
• 2015 Eagles @ Patriots. Pats down 14-35 at 11:09 4th quarter, came back to be down 28-35 with the ball at 1:02 left in 4th quarter.
• 2016 Patriots v Falcons SB. Pats down 3-28 at 8:31 3rd quarter, come back to win 34-28 in OT.

EDIT Let's compare our rate to other team's success when down 21 points at some point in the game from 2011 - present:

Source from PFR: Wins and Losses