For OP, it was December 16, 2007. That was the beginning of the end.
Jason Garrett's offense, which was hot and seemingly innovative at the time, ran into Jim Johnson for the second time and got exposed. I believe it was the first time they scored under 24 pts the entire season.
They never recovered.
Ultimately, I thought they ended up playing better in the Divisional against the Giants. The Giants were just so much better than what we gave them credit for at the time. I've made the argument before-- it's been shot down before, but the facts are there. The only reason they were 10-6 was because they were still coming together but had a brutal schedule where they played the three best teams in the league (Cowboys x2, Packers, and Patriots). The next year they started the season 11-1 after losing Strahan.