Ever since Roberto Di Matteo took over as Schalke manager six weeks ago, the team have been on their way up. And down. And up again. So called “Treppenläufe” (stair runs) in between the concrete stands of the crumbling Parkstadion where the Royal Blues conduct their training sessions have been added to the daily curriculum. Di Matteo has vowed to whip the Bundesliga side into the “fittest team in the league” after icily hinting that his predecessor, Jens Keller, could have done more in that respect. “There’s room for improvement,” said the former Chelsea midfielder and manager. Benedikt Höwedes, the captain and a World Cup winner in the summer, has backed that assessment, saying: “The physical sharpness was missing.”

Blaming sins of the past for the ills of the present, some local reporters have noted, is a way of life at Schalke. The much-storied, incredibly well-supported club from the post-industrial heartland of Germany have an unfortunate habit of never quite fully realising their true potential, which would only be half as unnerving for their fans if neighbours Borussia Dortmund had not done so much better with fewer resources in recent years. While Jürgen Klopp has transformed BVB into one of the most admired clubs in Europe since 2008, Schalke have been treading water furiously with six different coaches in charge.

Di Matteo is supposed to be lucky No7, the big name who brings sustained progress and maybe the odd trophy, the charismatic, energetic coach with broad enough shoulders to deal with the customary high-tension environment of Schalke 04. The Swiss-Italian knew full well what he was in for when he agreed to take the helm at the Veltins-Arena. “I don’t think anyone’s ever managed to calm things down at this club in 100 years,” he said at his unveiling.

The 44-year-old’s arrival was certainly greeted with plenty of excitement in Gelsenkirchen and a sense of pride. The editor of Sport-Bild, Alfred Draxler, hailed the signing of the 2012 Champions League winner as “the biggest coup for the Bundesliga since Pep Guardiola”. It also underlined the Bundesliga’s international appeal, Draxler felt.

Having grown up in the Swiss city of Schaffhausen, Di Matteo speaks perfect German. Public and players alike have been impressed with his unflappability. Reporters giggled admiringly when he calmly walked out of a press conference because someone had asked the same question – something about dedicated penalty takers – too many times. “He’s so cool that it’s almost frightening,” said Kevin-Prince Boateng. “As a player I find it very hard to read such calm, focused managers. That in itself makes everyone respect him.” His team-mate Marco Höger agreed: “The moment he comes into the dressing room with his calmness and his aura, everyone knows who’s the boss. Nobody dares to say anything.”

Di Matteo might enjoy more authority in the notoriously tricky dressing room than Keller, who was a little too accommodating. But on the pitch, the halo effect did not survive for long. After two wins in his first two matches, Schalke lost three of the next four before the international break.

They were firmly back where they started out before his employment: mired in mid-table inconsistency and in acute danger of getting knocked out in the Champions League group stage for the first time in nine years. Anything but three points against Chelsea, whom Di Matteo led to Champions League glory in 2012, on Tuesday night would spell real trouble for their European prospects. At least they were triumphant on Saturday, edging past Wolfsburg 3-2 from 3-0 up in what was a must-win game.

Critics have begun to wonder what it is Di Matteo is actually bringing to the table, better man-management aside. “Playing-wise, no signs of progress are discernible,” says Lothar Matthäus. Sport1 wrote that “on the whole, things seem to have deteriorated in comparison with [the Keller days]” after the 2-0 defeat at Freiburg. Di Matteo’s efforts have so far concentrated on making the team more compact but this has simply translated into a more defensive set-up that has left the key striker Klaas-Jan Huntelaar isolated. “We have to show more willingness to get forward,” the Holland forward told Kicker magazine.

Before playing Wolfsburg, Schalke were second from bottom in the Bundesliga in terms of shots at goal. They had also put in the lowest number of crosses, hit the fewest corners and conceded the most shots at their own goal. The performances have borne little relation to Di Matteo’s insistence that the club was “12th, 13th best in the world”.

The manager has started to play for time, citing a long list of injured players. He has warned that the club might “run behind [the competition] for the entire season”, promised to address the physical deficits more thoroughly in January and to use the winter break to decide whether the squad needs changes. “We have to see how far we can go until [December],” he said. More experienced operators would probably struggle to get ahead in the short term, too, but the coach at least needs to start to show that he can come up with solutions to go with the problems he has identified.

In the absence of better results, the initial optimism will increasingly give way to doubts over whether the poker-faced Di Matteo is really the gamechanger that the Schalke faithful crave. Horst Heldt, Schalke’s sporting director, has already felt moved to insist that the managerial change was “not something that’s meant for 14 days or three weeks but for a number of years”.

Di Matteo will do incredibly well to come within the latter bracket. No one has lasted two entire seasons at Schalke since Huub Stevens, “the coach of the century”, found success – and silverware – from 1996 to 2002.