On recent evidence they may face a similar wait before they do so again. A year after Stenhousemuir came to Rugby Park and ended their defence of the trophy at the first hurdle, it was another lower-league club's turn to inflict misery on them.
This was not what Allan Johnston and his players needed following a difficult start to a league campaign that has yielded just two points from their opening four games. They were watched last night by a disappointing crowd of 2033, although, should results not improve, it will soon be difficult to tell which fans are staying away in protest at the chairman Michael Johnston's stewardship of the club and which are simply not turning up because of the football on show. Hamilton Academical, the pacesetters at the top of the SPFL Championship, were worthy winners. Their hero was Mickael Antoine-Curier, that most peripatetic of players now on his 20th posting as a pro. Latterly of FC Atyray of Kazakhstan, the French-born striker is back at Hamilton for a third stint until the end of the season and marked his return to Scotland by securing the only goal of a scrappy game.
A stodgy opening period had seemed destined to finish goalless until Hamilton made the breakthrough three minutes before the interval. Ali Crawford was the provider, sending in a teasing corner that Antoine-Curier met flush on the forehead from around eight yards out. Craig Samson had no chance of keeping it out. It would prove enough to send Hamilton through to the third round. "I'm extremely proud, said Alex Neil, the Hamilton player-manager. "I thought we were the better side. I said beforehand that if we played to our potential we would have a good chance of winning the game and we did that. I thought we wanted it more."
There had not been many chances before Antoine-Curier struck although it was the visitors who looked the most likely to carve out a lead. Michael Devlin should have done better than head over the bar from another teasing Crawford delivery, while Antoine-Curier was penalised for an infringement as he rose to meet another cross. Kilmarnock offered little in response, a speculative shot from Rabiu Ibrahim - the home player who looked the most likely to create something - deflected wide by Grant Gillespie. It was little surprise Kilmarnock were booed off by their supporters at the end of a soporific first half.
The jeering initially had the desired effect. The home side looked brighter early in the second half, finally creating a goalscoring chance of note after 50 minutes. It was no surprise that Ibrahim was involved, the Nigerian uncorking a left-foot shot that Kevin Cuthbert did well to touch wide.
That would prove to be a false dawn, however. Instead of sustained pressure from Kilmarnock, it was Hamilton who continued to threaten. Antoine-Curier headed wide from another Crawford corner and, after he was substituted, only a poor touch denied his replacement Jon McShane from having a clear sight on goal. Another substitute, Andy Ryan, could have made the result emphatic but shot wide twice in injury time.
"It's disappointing, especially our first-half performance" Johnston said. "For all the good play in the second half we never really had that many shots on goal. We know we've got to improve. We've got to start picking up results as that first half wasn't good enough. We need to learn from this and make sure we get a result at the weekend."