Although their longevity and defiance of reason is both widely acknowledged and celebrated, Offaly are widely portrayed as a spent force now. The tag does not rest happily with players who have persistently responded to affirmations of their demise with stirring bigtime wins.
But another tame loss against Kilkenny, coupled with a fitful win against outsiders Derry has done little to alter the perception that Offaly are the sickmen of this year's All-Ireland semi-final series.
Paired again against a Cork side that remain ominously polished and low-key, there is an argument that Offaly's last realistic opportunity to conjure up another All-Ireland vanished with the loss in the corresponding fixture last year. Finely balanced in the drizzle with eight minutes remaining, it was a pulsating match that was poised for another memorable and improbable Offaly steal, but instead it was Cork's young guns who literally ran away from the then All-Ireland champions. That late energetic burst served to underline the mileage many of the Offaly players had accumulated over the decade.
"Well, that game was there for us and it wasn't," remembers Michael Bond, who, after guiding the team to the stunning triumph of 1998, stayed on for another year.
"Little things went against us that day. It is important to remember that Hubert Rigney and Kevin Martin were injured and, when the pool is as narrow as is the case in Offaly, the effect of every injury is magnified.
"John Troy had a questionable decision whistled against him, Cork swept up field and got a score, which was a massive two-point swing. And then the Cork forwards just hit everything that game from the sidelines almost.
"There was one occasion when Martin Hanamy had his man tied up, flush to the sideline and he hit an unbelievable point. Against Kilkenny, their shooting was quite poor.
"So it all added up. To be honest, I thought we were a better team last year than in 1998, but maybe we just didn't get the breaks."
Bond exhibited an intuitive understanding of what makes Offaly hurlers tick when he tapped into a latent energy in the midsummer of 1998 and remains a keen friend of the game there.
He will be in the stands on Sunday and, while he admits that his former charges are up against it, he warns that only the foolhardy would dismiss them.
"I am certain they will be smarting from the way they played in their last two games and how often have they managed to produce a performance from the blue which surprises everybody.
"It all comes back to their state of health. John Troy broke two fingers and then damaged an ankle this year, horrific for any player. After the form he showed last year, he is a huge loss.
"Brian Whelahan has had a niggling hamstring since early 1999. Kevin Martin has struggled. These are all devastating for Offaly.
"You saw Galway bring in Joe Cooney, David Tierney and Kevin Broderick off the bench last week, tremendous players that would walk onto any team. Offaly have no such luxury and their ability to compete is dependent on a healthy unit."
And Bond believes there are signs that the team are on the verge of cobbling together the resilience and stubborness of old.
"Johnny Dooley is flying all season and I think Johnny Pilkington is warming up again too, which delights me. And so many of the players - Michael Duignan, Joe Errity are adaptable. If Errity goes centre back, I feel certain he will be up to it. He is a natural hurler.
"It has been tough for Pat Fleury trying to settle on a team after such injuries, but he found new players who are starting to show their own potential. And they will be so tuned into this. The Derry performance was flat but the whole trend changed after Joe and Brian were introduced."
But that Offaly were level with Derry going into the final 10 minutes must have made for some grave reassessment after that quarter-final. This is their third consecutive All-Ireland semi-final appearance but this year, unlike the others, their presence seems to indict the lopsided nature of the championship struggle.
What counties like Waterford, Limerick or Clare would give for Offaly's passage. But the midlanders aren't responsible for the vagaries of the system. And rarely have they failed to enhance the championship with their flair for the unpredictable.
But the flat, prosaic nature of their campaign thus far lends credence to those who argue that the flame has, at last, left this remarkable bunch. If it transpires that they are left ragged by Cork on Sunday - a fate that many are predicting - surely that will trigger the end.
"People said in 1997 that the team were supposed to be finished and then, after the Leinster final in 1998, it was said that that was the final death knell," counters Bond.
"Last year, we came close and were maybe a little bit unlucky against Cork who went on to prove themselves in the final. And that was seen as the swansong.
"It hasn't happened yet. All Offaly have to keep doing is find one or two new players each season. The majority of the established players still have a lot to offer and I can't see them breaking up just yet."
But surely it is too much to expect a rising on Sunday. Surely the All-Ireland champions just have too much.
"Cork are probably an even more difficult prospect last year. But I wouldn't be all that surprised to see another great Offaly rally.
"They have been in these type of situations before and, if they hit gear, it should be fascinating."