And so the misery continues. Albion are ending the season with an almighty whimper, especially at Withdean.
Bradford gave themselves a fighting chance of staying up with a vital victory, only their second in 16 matches. The Seagulls would be down near the basement with them without their impressive away form. They have now won only once in 11 games at Withdean and scored in only two of the last nine.
The problems do not end there. Bas Savage is the only Albion player to have scored in the last ten matches, a terrible sequence stretching back to Nick Ward's winner against Nottingham Forest in February.
Yet again, after a promising start, the Seagulls failed to get enough balls into the opponent's box and to create chances.
The final whistle was greeted with anger and boos from season ticket holders in the South Stand, which was hardly surprising, particularly as Bradford kept their first clean sheet since January 6.
Joel Lynch was absent from the Albion squad for only the third time this season due to glandular fever.
Alexis Bertin returned to the holding role in the midfield diamond after missing Monday's 2-1 defeat at Tranmere with a groin injury.
Adam El-Abd moved to rightback and Zesh Rehman into the middle alongside captain Guy Butters, the third different central defensive partnership in as many matches.
Bradford made one change to the team held at home by Oldham on Monday. Joe Colbeck was ruled out by the red card he received in that game, so Omar Daley came in to the midfield.
Former Bradford striker Ian Ormondroyd, now working for a radio station in Yorkshire, described the match beforehand as one of the biggest for City since their relegation from the Premiership as recently as May 2001.
Conventional wisdom suggested the visitors had more motivation, given their perilous position, but the Seagulls, as manager Dean Wilkins pointed out, still had pride to play for and, in some cases, futures.
The starting line-up included four of the 15 players out of contract at the end of the season.
El-Abd is not one of them but he showed customary commitment inside the opening minute with a crunching but legitimate challenge on Billy Paynter which left the Bradford forward, on loan from Southend, in need of prolonged treatment.
This seemed to disrupt City in the early stages. They seemed more concerned about whether Paynter would be able to continue than concentrating on keeping at bay an Albion side starting in much perkier manner than at Withdean in recent weeks.
Rehman headed over from a free-kick by Sam Rents before Bradford keeper Donovan Ricketts was tested.
Jake Robinson, rejuvenated at Tranmere, escaped from Bradford skipper Mark Bower to deliver a penetrating cross from the right wing.
Savage, who should be better in the air than he is for his size, met it with a decent downward header which Ricketts managed to cling on to.
Bradford were allowing the Seagulls plenty of room and they took full advantage, dominating possession without being quite able to produce a finishing flourish.
Doug Loft was too high with an angled drive from a careless clearance by Eddie Johnson, a centre forward turned into a central midfielder.
Bradford barely threatened in the opening half-hour but they were given encouragement on the break by some sloppy Albion play, with Loft, Butters and Tommy Fraser all guilty of either being caught in possession or giving the ball away cheaply.
Fraser's looseness proved costly. It led to a corner from which Bradford took the lead against the run of play in the 34th minute.
Kelly Youga, the City leftback on loan from Charlton, connected from Johnson's flag kick with a looping header over Scott Flinders and against the underside of the bar.
The ball bounced down for Paynter, still limping from his early injury, to nod in his fourth goal for Bradford from close range.
The Seagulls almost equalised in similar vain three minutes later when Butters' header from a free-kick by El-Abd looped on to the upright via the faintest of touches from the diving Ricketts.
Wilkins' men found themselves in familiar territory at the break. The last time they scored the first goal at home was against Carlisle at the end of December.
It took a while for Albion to regain the momentum they had earlier in the match. Dean Cox epitomised their frustration with a booking for a foul on Daley early in the second half, his eighth yellow card of the campaign.
The introduction of Alex Revell in the 56th minute in place of Fraser, who seemed to be suffering in the heat, coincided with a more forceful spell from the Seagulls.
Revell, who requires a hernia operation at the end of the season, came close to levelling twice in quick succession. He had his back to goal from a low cross by Rents, with Bradford caretaker manager David Wetherall marking him closely.
Revell still managed to turn and get in a shot which clipped the top of the bar.
A minute later the former Braintree marksman volleyed over when Robinson pulled the ball back to him at the near post.
Moses Ashikodi nearly provided the second goal Bradford needed to calm their nerves with 15 minutes left. The on-loan Watford teenager just failed to divert on target a low cross from Paynter.
Albion, desperate to salvage something to alleviate their home horrors, threw on Joe Gatting in the closing stages at the expense of Butters but it was to no avail as Bradford held on for a priceless victory.
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