It is Thanksgiving week, and Thanksgiving week for the Washington Redskins means relevant games are no more, promise is in the past and potential satisfaction is put off till next year, or the year after, or the year after that — a perpetual holding pattern.

That much was assured again after the Dallas Cowboys, once the other half of the National Football League’s most mean-spirited rivalry, came to FedEx Field on Sunday, allowed the Redskins both a measure of false hope and an overtime kick that could have won the game, and took a 27-24 victory anyway.

The details can be parsed, and in some corners they will be over the course of the holiday week. But the particulars, at this point, hardly matter. It was the Redskins’ sixth straight loss. Six games remain in the season. So the most meaningful questions surrounding the franchise over the holidays are: Will there be another victory this year? Is the right leadership in place? And, when’s the draft?

“It’s difficult, man,” linebacker Brian Orakpo said afterward in a locker room that was quiet enough to hear the zipping of equipment bags. “We . . . shoot, I don’t know. It’s just difficult.”

There are, by now, very few reasons for veteran players to offer detailed dissections, because at some point one season blends into another, and the losses become almost indiscernible. The difference this year: With two-time Super Bowl winner Mike Shanahan in his second season as head coach, and with offseason moves that addressed several weaknesses on defense, players and coaches were palpably optimistic two months ago, particularly after winning three of their first four games.

Now, the team is in the midst of its longest losing streak since 1998 — the longest of Shanahan’s 18 seasons as a head coach — and a peek toward 2012 seems appropriate.

“I’ve never been part of a losing streak like this,” defensive captain London Fletcher said. “I know a lot of guys have never been a part of this. I know Coach Shanahan hasn’t been part of this.”

To be sure, for one of the few times all season, there were developments worth cheering Sunday. The offense, which had scored just one touchdown in the previous three games combined, managed an efficient fourth-quarter drive to tie the game with 14 seconds left, and produced more points than it had all year. Quarterback Rex Grossman, back in the starting lineup for the second straight game, threw for two touchdowns and ran for another.

Had place kicker Graham Gano converted either of two missed field goals — including a 52-yarder in overtime — the losing streak could have been over, and the focus could have been on some unexpected improvements.

“I’d rather talk about silver linings on Wednesday or something,” Grossman said. “It’s just frustrating right now.”

But Sunday’s loss will nestle into a season that puts Washington’s glory years further behind, and becomes part of a growing legacy of disappointment. At the Redskins’ Ashburn training facility, three Super Bowl trophies still sit prominently in a display case in the lobby. But the last of those arrived after the 1991 season. The kids who sat with parents in the stands Sunday have only heard tell of them, even as jerseys throughout the stands — Theismann and Green, Riggins and Monk, greats long since come and gone — showed there are those who remember when.

With their record now 3-7, and with injuries to several key players — notably, tight end Chris Cooley, running back Tim Hightower, offensive lineman Kory Lichtensteiger and wide receiver Santana Moss — the Redskins are almost certain to miss the playoffs for the fourth straight season, and the 16th time in the last 19 years. Lose once more, and they would ensure that since their last division championship — which came a dozen years and six coaches ago — they would have just two winning seasons.

Shanahan was the man owner Daniel Snyder hired to alter that history. He has never endured a worse season than last year, his first with the Redskins. Sunday, he was left to restate his faith in his team and stave off a full-on meltdown.

“I feel very good about the guys we have in that locker room,” Shanahan said. “As much character as I’ve been around on a football team. Even with adversity, there’s guys doing everything they can.”

To what end?

“It’s one thing to fight,” Fletcher said. “But it’s another thing to fight and win.”

In some cases, there is reason to believe being bad is good, because it could result in high picks in next spring’s college draft. This year, the prize is Stanford quarterback Andrew Luck, who would fill precisely the position that is the Redskins’ greatest need, not to mention their greatest source of instability for a generation.

But the Redskins can’t win for losing: Indianapolis hasn’t won any of its 10 games this season, and the hapless Colts have a significant edge toward securing the top pick, which goes to the team with the worst record the previous year.

So the current group is left to slog forward, even after Sunday, even after another loss. They will meet again Monday morning to discuss their mistakes, painful as they may be. The season will continue.

“We’ve lost in a lot of different ways,” defensive lineman Barry Cofield said. “This is obviously the hardest one of all.”

In overtime, when Dallas place kicker Dan Bailey’s field goal sailed toward the goal posts and the officials signaled that it was good, ending the game, Shanahan left the sideline slowly. He stared incredulously at the uprights, wondering if the ball had in fact been wide.

The officials did not waver. So Shanahan turned toward midfield, toward a handshake with Dallas Coach Jason Garrett, and then began a trudge to the locker room, where more work — and the rest of a difficult season in a string of difficult seasons — awaited.