But there is a new fear for the Hammers after furious fans invaded the pitch upon the final whistle and screamed abuse at the chairman, Terrence Brown, and his directors. The protest came seconds after Kevin Russell's last-minute Wrexham winner confirmed the latest Upton Park debacle.
Peter Storrie, the managing director, is worried the Football Association could take disciplinary action even though the demonstration - by about 400 fans who continued their protest outside the main entrance - came after the final whistle.
Rebel fans are planning another demonstration for Arsenal's visit on Wednesday night, aimed at forcing the board to accept multi-millionaire former bookmaker Michael Tabor's much-publicized offer of a cash injection in exchange for putting in his own man to run the club.
Five years ago - when fans mounted a campaign which eventually stopped West Ham's plan to finance the building of a new stand through a supporters' bond-holders' scheme - two home matches were disrupted by pitch invasions, resulting in an official warning to the club over crowd control.
The FA was in correspondence again with West Ham only seven weeks ago after fans came onto the pitch when the captain, Julian Dicks, scored a late penalty equaliser in the 2-2 draw with Manchester United.
Disciplinary action was again deferred but Storrie said: "It amounts to us still being under a suspended sentence from what happened a few years ago. As, this time, it happened after the final whistle we are hopeful the FA will take a reasonable view - but they might not. This is bound to be reported and we'll just have to wait and see if we face a charge."
Slaven Bilic, the big Croatian defender who has been one of Redknapp's few successes among a flurry of foreign signings over the past year, stepped out into the Upton Park forecourt, ignoring police advice, to appeal for calm and unity among the protesting fans.
Bilic, however, has become another problem for Redknapp after his eighth booking of the season on Saturday. He is now facing a two-match suspension.
Redknapp, whose side have plunged into the Premiership's bottom three after just one win in 15 matches, said he would walk away from West Ham if "people don't want me here and the chairman thinks it is the best thing for the club".
But rumours of an emergency board meeting to discuss his future on Saturday night can be discounted and Storrie confirmed that West Ham are backing Redknapp with hard cash as he seeks to boost his strike force. Offers are already in to Newcastle for their striker Paul Kitson and Stoke for the 21-goal Mike Sheron, both rated in the pounds 2m-plus bracket.
Goal: Russell (90) 0-1.
West Ham United: Miklosko; Breacker, Bilic, Dicks, Williamson, Bishop, Lazaridis (Porfirio, h-t), Hughes, Lampard, Ferdinand, Jones. Substitutes not used: Bowen, Sealey (gk).
Wrexham: Marriott; McGregor, Hardy, Hughes, Humes, Carey, Chalk, Owen (Russell, 75), Connolly, Watkin, Ward. Substitutes not used: Jones, Morris.
Referee: S J Lodge (Barnsley).
Bookings: West Ham: Bilic. Wrexham: Hughes, Humes.
Man of the match: Humes.