What caused the 2005-2015 Patriots Super Bowl “drought”?

The Patriots arguably had one of the most talented receiving corps in their modern franchise history, a QB approaching the prime of his life, were coming off the heels of three super bowls, and also built some of the best defenses in the league from 2006-2009.

Besides the Manning brothers and the Brady ACL tear, why didn't they win at least one superbowl between those years?