Victoria Thompson (48) and husband Trevor (54) were told by Appeal Court judge, Lord Justice Ward: "The lesson is never learned that those who fight for their principles frequently end up paying for them."
The Thompsons have spent tens of thousands of pounds disputing with Graham Collins and Susan Lloyd over whether the boundary between their homes in Hatcliffe should be drawn through the centre of a laurel hedge or a few feet further back.
Describing it as "another expensive boundary dispute", Lord Justice Ward told London's Civil Appeal Court: "Each of the parties have spent in the region of £40,000 in bringing their case to this court, far more than the land in dispute could ever be worth."
The court heard disagreements began soon after the Thompsons moved to Hatcliffe in 2002, with neither side able to agree where the boundary lay.
As reported, the case came before Grimsby County Court in December 2007, where Recorder Gibson ruled the boundary should be drawn through the middle of a laurel hedge and a bay tree.
He left it down to the neighbours to discuss the minutiae of the line – but they couldn't come to terms and were back at the County Court in June last year.
Recorder Gibson then drew the line exactly, creating a zig-zag border between the houses.
Mrs Thompson – who works for Humberside Police – and her husband remained dissatisfied, however, and appealed against that decision before Lord Justice Ward, Mr Justice Keene and Mr Justice Collins.
Their barrister, Ian Pennock, argued that the line drawn by Recorder Gibson defied common sense and urged the judges to reconsider it.
"No reasonable layman would, or could, have thought he was buying land with such a pronounced zig-zag boundary or consented to the same," he argued.
"As a matter of common sense, how would he construct a fence along such a boundary without it looking absolutely ridiculous?"
But Jonathan Rodger, representing Mr Collins and Miss Lloyd, said that the laurel hedge was a prominent feature of the landscape and it made sense as a boundary line marker.
Rejecting the Thompsons' appeal, Lord Justice Ward said Recorder Gibson had been entitled to come to the decision he did.
Speaking outside court, Mr Collins, an accountant, said the case had "ruined our careers and our finances. This has caused us a great deal of anxiety and stress and we are absolutely relieved it is over".