A big reason the Skins remain competitive right now is because of how awful the division is. The fact that the 3-8 Cowboys are still mathematically in contention speaks volumes about just how bad the division is. As far as QB's, while Cousins is playing somewhat better right now...just last season, he was benched in favor of Colt McCoy. RGIII of course had a great rookie season & then fell of the map. The Skins haven't yet escaped the flames when it comes to long-term QB stability/consistency.
It's also staggering to look across the league & see how many 4-7, 5-6, 6-5, etc. teams there are...and how many are still in contention for playoff spots.
The Boys/Skins rivalry is historically unpredictable regardless of records.
Though I know the OP was referencing QB purgatory...this whole season has been 'hell'. It's not simply losing Romo twice...though that's the biggest reason. It's also injuries to Dez, Scandrick, Dunbar, T. McClain, Claiborne, Gregory, Lee, etc. This team has had chances to win every game they've played with the exception of the Panthers and Pats games.
Unfortunately, it was Romo's turnovers that led to a big Panthers win...with Carolina's defense scoring 14 points via returning 2 of Tony's 3 Int's for TD's. The 3rd put the defense in a bind, but they held them to a FG. Carolina scored one (1) offensive TD. Cam wasn't the biggest reason they won...their defense was. Newton completed 16 passes for 183 yards & had 1 rushing TD vs. the Boys...but he did convert a couple of long distance 3rd downs. The Panthers defense was also dominant vs. the Skins, forcing 5 turnovers that led to 27 points. But in that game, Newton also threw 5 TD's to five different receivers in their 44-16 win.
Turnover differential has played a major role in the Boys losing. Last year they were among the better teams in terms of turnover differential...whereas this season they're dead last. The 4th quarter/OT defensive lapses have doomed them on a few occasions as well. It hasn't all been the player under center, though a healthy Romo all season means the Cowboys are very likely 'easily' winning the pathetic NFC Least...as he is able to help cover up some of the other deficiencies.
Lastly, even teams with good to great QB's have endured losing streaks. Prior to winning 15 straight going back to last season...the Panthers lost 6 or 7 straight with Newton. The Packers have lost 3 out of their last 4 with Rodgers. Atlanta started out 5-0, but has gone 1-5 in their last 6 games...all with Ryan as the helm. San Diego owns the same 3-8 record as the Cowboys, despite having Rivers for the entire season. The Saints are a train wreck despite having Brees for all but 1 game.