Sean Dyche's side have earned plenty of plaudits for their style of play this season, but not enough goals or points.
When they stunned champions Manchester City 1-0 in March they were one point behind 17th place and survival appeared to be well within their grasp.
Five defeats and a 0-0 home draw with Tottenham Hotspur in their next six matches, however, leaves the humble Lancashire club needing a sporting miracle.
With three games left to play they have 26 points, compared to 17th placed Hull's 34. They must beat Hull, Stoke City and Aston Villa and hope for favours elsewhere.
Despite their predicament, Dyche said his team remains motivated and midfielder Matt Taylor insists the fight goes on.
"There's three games left and we'll continue to fight," Taylor told the Lancashire Telegraph.
"We won't feel sorry for ourselves. We'll dust ourselves down and go again."
While Burnley's Premier League status looks almost certain to last only one season, as it did in 2009-10, fellow promoted side Queens Park Rangers are also in dire straights, although Leicester City look like surviving.
QPR, on 27 points, will be doomed by the time they travel to Man City on Sunday, should Hull beat Burnley, Aston Villa beat West Ham United and Newcastle United beat West Bromwich Albion the day before.
Third from bottom Sunderland, who are a point behind Hull with a game in hand, could put the jitters up the teams just above them with victory in Saturday's early kickoff at Everton.
A Sunderland win against Roberto Martinez's side would take them, for a few hours at least, above free-falling North East rivals Newcastle United who have lost eight league games in a row and are spiralling out of control.
Newcastle, in 15th spot with 35 points, had two sent off in the 3-0 capitulation at Leicester last week, after which manager John Carver suggested defender Mike Williamson had got a red card on purpose.
Such is the disarray at St James' Park that skipper Fabricio Coloccini wrote an open letter apologising to the club's fans.
"Players and staff have come together in order to leave all past problems aside and to focus 100 percent on the three 'cup finals' that we have left," he said.
With Chelsea already champions and Arsenal and Manchester City scrapping for second place, the only real intrigue at the top is whether fourth-placed Manchester United can clinch a place in the top four, having lost three consecutive games.
Victory at Crystal Palace on Saturday would ease their nerves.
(editing by Justin Palmer)
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