ANY lingering hopes of promotion from the Dr Martens Eastern Division that the Linnets had went after Saturday's draw.
The most points they can get is 82, and second-place Dorchester already have 84.
Lynn managed a point after twice conceding a soft goal. On target were captain Glen Fuff and a peach from midfielder Richard Woodrow.
Linnets boss Peter Morris felt it was a case of two points dropped, and said: "That was as good a performance as we've given away from home this season.
"I'm disappointed that we haven't returned home with all three points.
"We dominated for long periods, but conceded a soft first goal and went to sleep for their second near the death."
Lynn lost two more players to injury in the first quarter-hour, and defender Mark Burrows and striker Chris Bacon were due to miss yesterday's derby with Spalding
A second error in two games by stand-in keeper Simon Nobes meant the hosts took the lead in the eighth minute.
Nobes dropped a cross, leaving the Dr Martens Eastern Division's leading scorer Norman Sylla with a tap-in for his 32nd strike of the season - "a lorra, lorra goals" for Sylla.
As Lynn were still reeling from having to replace two players, Banbury almost got a second.
A long ball found Sylla, who lobbed the ball over Nobes, but the strong wind held the ball up just enough for Fuff to clear off the line.
Dazzling midfielder Lee Stevenson with a header went close and Dave Staff beat the offside trap but keeper Simon Tricker dived to his left to save.
Fuff grabbed the equaliser after 36 minutes, heading home a Staff corner, but Banbury vigorously protested that Fuff used his hand.
Mark Paul, who had come on for Bacon, was set up by Stevenson but was denied by a superb close-range stop from Tricker eight minutes into the second half.
Carl Holmes headed over and Jack Defty was also wide of the mark. Fuff struck from 35 yards, but Tricker saved with his legs.
At the other end Lewis Blois cleared off the line from Wayne Blossom's 71st minute header.
Seven minutes later The Walks outfit took the lead. Blossom passed back to Tricker, who mis-hit his clearance and Richard Woodrow volleyed home from 25 yards.
But with just four minutes to go Lynn were prevented from becoming the only side to do the double over Banbury this season.
Fuff missed a high ball and George Redknap ran behind him. Nobes thwarted his first effort, but the striker made no mistake with his second attempt.
Lynn: Nobes, Holyoak, Blois, Burrows (Jones 78), Fuff, Defty, Woodrow, Stevenson, Bacon (Paul 12) Staff, Holmes. Subs riot used: Weston, Blake.
Banbury: Tricker, Fuller, Blossom, Sullivan , Allen, O'Neill (Ibrahim 89), Corbett, Stanbridge, Sylla, Redknap, McKay. Not used: Stridder, Brock.
Att 319. MoM: Lee Stevenson. Referee: Graham Scott (Abingdon).