When do NFL teams get eliminated from the postseason?

Once a team qualifies for postseason play, they must continue to win. You lose, you're out. As for qualifying for the postseason, there is no set cutoff date. Some teams are already mathematically eliminated this season. Just about every season, it comes down to the final Sunday of the regular season for a handful of teams.

As of right now, the Raiders and 49ers are eliminated from the postseason.

it happened to the packers tonight

@comment, the packers suck and are done

sometimes it can go as long as the last week of the regular season.

So normally you take the worst team in the wildcard and you see if the team can still finish with a better record if they win all their games and that wildcard team loses all their games. Now without any Division Champions yet you also have to consider if the team can still win the division. I'd say next week Oakland will officially be out(they could technically finish 7-9 now, 2nd wild card is at 6 wins, Raiders likely lose to KC next week and Baltimore or Indy likely win). SF and Arizona will likely officially be out pretty soon as well, maybe next week.

when they are mathematically out of it. Meaning, even if they win every game from then on out they could not get in the playoffs.

if a team is in the playoffs, they are eliminated when they lose a game.