Well, it had to come at some stage, and on Saturday it finally did.
No, not the end of City's fabulous unbeaten run. Rather a goal for rejuvenated striker Mark Sertori.
While the Minstermen upped their undefeated streak to an impressive eight games, the one-time centre-back headed his first goal since former manager Neil Thompson brought him to the club - as a defender - in September.
The strike - the only goal of the game - came on 80 minutes and was fittingly the product of City's follicly-challenged midfield pair.
Kevin Hulme and Steve Agnew have probably got less hair than any other Third Division engine room, but their record of never having been beaten when starting a match together remains intact.
Hulme was at his brilliant, effervescent best in midfield, covering every blade of grass, tackling everyone in a striped shirt and always looking to burst forward.
And although Agnew's class wasn't always to the fore, it was from his cross, from Hulme's touch, that saw Sertori charge in to head home.
Although 'keeper Steve Book got his hand to the ball, he couldn't stop it nestling in the bottom left corner, to give the Mancunian his only goal in ten starts as a striker.
It was richly deserved for Sertori, repayment for his hard work on Saturday and in his recent unstinting efforts, which - despite being previously goalless - had not gone unnoticed by the City faithful.
Playing on a marvellous carpet-like pitch which stayed remarkably healthy despite the continuous rain, York again defied their lowly league standing.
Indeed, as the form team in the third division, the supporters, management and, more importantly, the players now enter games expecting to win - even against promotion-chasing teams like Cheltenham.
It's a shame the turnaround in fortunes didn't begin earlier in the campaign, but it at least bodes well for next year.
The brick outhouse-built ex-Burnley barrier was probably the pick of an excellent City defence, but to say Cheltenham did not deserve anything from the game would be unfair, because they could, on another day, have scored six.
The fact they didn't was down to poor finishing thrice, bad luck once, and the brilliance of City 'keeper Alan Fettis at either end of the match.
Indeed, the hosts won the corner count 9-2 and in a blistering opening burst threatened to tear City apart.
On nine minutes, York-born Neil Grayson - with his only telling contribution before being substituted after the restart - sent Martin Devaney clear, but, with just Fettis to beat, he screwed his shot wide. Two minutes later, Fettis superbly pushed a Russell Milton header over the top.
A goal feast looked imminent but instead City proceeded to kill the hosts' fervour. Even disruption to the Minstermen back three - as Chris Fairclough took the place and captain's armband of the injured Barry Jones - did not alter matters.
However, Cheltenham did create four more good chances after the break.
Firstly, Devaney fired wide following a John Brough flick-on, then Mark Freeman sent a free header from eight yards trickling towards the corner flag, and then Mark Yates sidefooted narrowly wide from the edge of the box.
And finally, as the clock ticked down with City 1-0 up, Freeman stooped low to fiercely head the ball towards the bottom right corner, only for Fettis to spring to his left and magnificently palm the ball around the post.
That gave the City custodian a fifth clean sheet in six games and the third on the trot for the Minstermen for the first time since November 1997 when Tim Clarke, now at Conference tile chasers Kidderminster Harriers, produced a similar shut out.
At the other end, City created nothing in a workmanlike first half, an early Conlon shot over the bar and a tame Sertori shot being their only efforts - and barely notable ones - on goal.
But they came more into the match after stifling the hosts' early onslaught and came more into their own after the break.
Sertori saw a good chance on the hour well saved by Book, after which Hulme thought he had won the first of two possible penalties, when seeing his header from a far post Agnew cross apparently strike a stray defensive hand. The referee awarded only a corner.
Three minutes later, Hulme raced onto an Edmondson ball, rounded the golden-haired 'keeper and was brought down - only to be brought back by a disputable flag.
The goal, if not blatantly on the cards, concluded a brief period upon which the Minstermen had stamped their authority.
The speedy John Williams and Colin Alcide had both recently entered the fray to boost City's attacking options, and both had made an impact - Williams firing a cross into Book's hands and Alcide looping a header into the custodian's arms - within five minutes of the deadlock-breaker, the build-up to which the former had also played his part.
Sertori thence broke his duck and, to counter Cheltenham's last-ditch attacks, promptly became the fourth centre-back in City's back line as Fettis and co held out.
It all allowed the City faithful to sing and dance in the rain in the warm knowledge that not even the strictest of mathematicians can now see them relegated.
YORK CITY: Alan Fettis 7, Barry Jones 7 (Chris Fairclough 38 mins, 7), Peter Swan 8, Mark Bower 7, Darren Edmondson 6, Steve Agnew 6, Kevin Hulme 8, Christian Fox 6 (Colin Alcide 69mins, 7), Peter Hawkins 7, Mark Sertori 8, Barry Conlon 6 (John Williams 65mins, 7).
Subs not used: Russell Howarth, Scott Jordan.
Goals: Sertori 80 mins.
Bookings: Conlon 34, Edmondson 45.
Statistics: Half Time: 0 Corners: 9 Shots on Target: 3 Fouls Committed: 17
Evening Press Unique Pub Man of the match
Kevin Hulme: Got through enough work to make up for missing the remaining games of the campaign. Will be hard to replace in the engine room.
CHELTENHAM TOWN: Steve Book, Mike Duff, Jamie Victory, Chris Banks, Mark Freeman, Lee Howells, Neil Grayson (John Brough 48), Mark Yates, Neil Howarth (Anthony Griffin 86), Russell Milton (Hugh McAuley 81), Martin Devaney.
Subs not used: Bob Bloomer, Shane Higgs.
Goals: None.
Bookings: Banks 34
Statistics: Half Time: 0 Corners: 2 Shots on Target: 3 Fouls Committed: 12
Attendance: 4,722
Referee: Scott Mathieson (Stockport)
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