The relegated Rocks lost 2-1 at Concord on a night when Sussex rivals Whitehawk joined them in going down from National League South.
The home side have been in relegation trouble themselves but are almost safe after defeating Jack Pearce's team in Essex.
Ibra Sekajja scored the Rocks goal late on after Concord had taken a two-goal lead.
Bognor have three games left and the best they can hope for is overhauling Whitehawk so they do not finish bottom. The Hawks' fate was sealed with a 4-3 loss at Braintree.
Elsewhere, there was better news for a number of Observer-area sides - particularly for Bosham, who are through to the final of the SCFL Division 2 Cup.
Facing Cowfold at Steyning in the semi-final, Bosham reached the final of a competition they won in 2015 and 2016 with goals from Graeme Dowden and Grant Radmore after the opposition had taken a second-half lead.
In SCFL action, two goals from Rob Hutchings and one from Scott Jones earned Chichester City a fine 3-1 home win over Three Bridges, a boost after two straight defeats for Miles Rutherford's team.
In division one it finished 2-2 between Midhurst and Selsey at the Rotherfield. Kieran Carter and Mark Broughton put the Stags into a 2-0 lead but Mohamed Seye and Cameron Corell earned the Blues a point.
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