But the Clarets can take great heart from the nine clubs from seasons gone by that have proven that it’s never over until it’s over!
Many sides since the Premier League’s inception have been treading far murkier waters at this stage of the season and have managed to snatch survival from the jaws of relegation.
Here are the teams who have done it best.
1. Oldham Athletic 1992-93
Oldham Athletic are the holders of the Premier League's first ever 'Great Escape'. The Latics looked down and out as the inaugural campaign reached its conclusion with Joe Royle's side needing to overturn a six-point deficit with just three games remaining. They were also eight points adrift of Crystal Palace, who were eventually relegated by virtue of goal difference in a sensational final-day decider. Oldham won their final three games, beating Aston Villa and Liverpool before seeing off Southampton in a seven-goal thriller as the Eagles lost out to Arsenal. Both sides closed the season on 49 points, which remains the highest points tally by a relegated top-flight side. Photo: Clive Brunskill
2. West Bromwich Albion 2004-05
The Baggies became one of only three clubs in Premier League history to survive after being bottom of the pile at Christmas. Bryan Robson's side were eight points from safety with two games in hand at the beginning of March. From that point — starting with a 2-0 win against local rivals Birmingham City at The Hawthorns — they collected 16 points from 11 games, which was the fifth best form in the division over that period, to keep their heads above water. Incredibly, West Brom were still bottom on the final day of the season, but beat Portsmouth 2-0 on 'Survival Sunday' to complete a miraculous turnaround. Photo: Matthew Lewis
3. Portsmouth 2005-06
Just like Burnley, relegation-threatened Portsmouth had won just four games in 28 attempts heading into the final stretch of the campaign. Pompey were also the lowest scorers in the division and found themselves eight points off 17th place West Bromwich Albion. However, Harry Redknapp's side flipped their season on its head by averaging two points-per-game from their final 10. Their run started with a 2-1 win over Manchester City while safety was assured on the penultimate weekend of the term as they beat Wigan Athletic 2-1; the fourth game during that spell in which they'd overturned a deficit to secure points. Photo: Ben Radford
4. West Ham United 2006-07
West Ham United managed to overcome a 10-point deficit with just nine games remaining to wrap up safety on the final day of term. The Hammers picked up more points during that final stretch (21) than they did in their opening 29 matches of the season (20). It all came to an exhilarating conclusion at Old Trafford as they defeated Manchester United 1-0. Argentinian international Carlos Tevez had a hand in a league high 10 goals in as many appearances at the back end of the season, including the winner at the Theatre of Dreams, to inspire a 'Great Escape'. Photo: PAUL ELLIS