The Rocks went so close to salvaing a point in a dramatic finish to their visit to face Gloucester City - having looked down and out at 3-0 down.
Goals in the final few minutes by Ibra Sekajja, from the spot, and Keaton Wood, pulled it back to 3-2 and Sami El-Abd almost secured a remarkable draw.
As it was, the defeat leaves Bognor on the brink - they could be relegated when they face St Albans at Nyewood Lane on Tuesday night.
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Bognor travelled to Evesham United's ground, where Gloucester are ground-sharing, knowing time was fast running out in their battle to stay in National League South.
With El-Abd back in the starting line-up, Jimmy Muitt and Sekajja were both on the bench. An early knock forward by Richard Gilot almost found Ollie Pearce but he couldn’t quite latch on to it. For City, Ed Williams passed to Kieran Thomas, whose cross was nicely gathered by Dan Lincoln. Thomas fouled Calvin Davies but the free-kick came to nothing.
Pearce's curling free-kick was headed out on 13 minutes and at the other end Joe Parker smashed the upright. Pearce's back-heel was rolled towards Justin Amaluzor and the ball bounced to Doug Tuck, but his ball back inside the box bounced out of play. Williams had a shot blocked.
Lincoln gathered another high in-swinging cross from Thomas, then struggled to deal with an El-Abd backpass that almost outwitted the goalkeeper. Amaluzor won a corner and Pearce’s cross was headed down by Charman but cleared.
Tuck was booked for a trip on 32 minutes. For City Chris Knowles hit a looping bouncing ball on to the top of the net with a strike that dipped late. Amaluzor cut the ball back to Pearce, who struck it from an angle and forced James Hamon into his first save of the day on 36 minutes.
On 38 minutes Bognor were caught napping at the back when Charman and Keaton Wood's mix-up allowed Tigers through and Joe Parker's low strike flew beyond the outstretched Lincoln. Joe Hanks was booked for dissent on 42 minutes for the hosts.
Bognor had a great chance when Amaluzor set Pearce through just before half-time, but Hamon was brave to deny him, rushing out of his goal at his feet to scupper the chance. HT 1-0
Knowles' pass saw Parker run through but his chip over Lincoln flew over the bar shortly after the restart. Pearce needed treatment and had to be replaced by Sekajja on 50 minutes after appearing to twinge his groin. Thomas received a booking after a challenge with El-Abd on 53 minutes. Then Harvey Whyte smashed the ball high over the bar from way outside the box.
On 57 minutes the Tigers extended their lead. A ball in from Hanks found Williams who fired at goal and the ball bounced back out to an onrushing Parker, who slammed it high into the net despite Lincoln getting something on it.
Parker committed Lincoln into a save from long-range before the same striker smashed another wide on 65 minutes. Ben Swallow replaced Charman on 68 minutes. The sub was soon involved, with a cross towards Amaluzor but it flew out.
The third goal came on 77 minutes when Ed Williams' corner found Matt Williams, who glanced a neat header beyond Lincoln. It seemed all over for Bognor. A hopeful ball across by Sekajja saw Swallow's scissor kick miss - then Swallow’s left-sided cross was nodded over by sub Tommy Scutt.
On 88 minutes, Bognor won a penalty when Amaluzor was fouled following a Swallow corner. Sekajja slotted it home beyond the outstretched hand of keeper James Hamon. It was the Rocks' first goal away from home in almost 500 minutes of football, their previous one having been Muitt's equaliser at Hungerford on January 27.
The Rocks continued to push and on 90 minutes they got a second. A free-kick from Swallow was swung in and Wood nodded in at the back post to the delight of the travelling support.
Could the Rocks claim a point? Almost... Swallow's ball was aimed at Scutt but it bounced through to El-Abd, who struck it first time with his left boot and forced a quick diving save from Hamon.
That was the last action and the Rocks had lost - but at least the travelling fans had seen something to cheer. Sadly, the club's relegation seems certain to arrive very soon.
Rocks: Lincoln, Whyte, Davies, Tuck, El-Abd, Wood, Gilot (Scutt 80), Block, Amaluzor, Pearce (Sekajja 50), Charman (Swallow 68). Subs not used: Muitt.