Placards reading "That is our record! Ra-Ra-Ra Tasmania (The Original)" and "Save the record for Tas!" were laid out in front of Berlin's Olympic Stadium before Schalke's 3-0 defeat to Hertha Berlin on Saturday.
Christian Gross, Schalke's fourth head coach this season, got off to a losing start as Arsenal loanee Matteo Guendouzi, Colombia striker Jhon Cordoba and his replacement, Poland forward Krzysztof Piatek, scored for Hertha.
"I hope we can still sign in one or two players, who could bring a bit of personality," said Gross after watching his new team's latest loss.
Schalke, who are bottom of the league, boosted their squad last Thursday by re-signing defender Sead Kolasinac, who did not face Hertha, on loan from Arsenal.
They host Hoffenheim next Saturday and are now one match from equalling the league record, long held by Tasmania Berlin, who went 31 matches without winning in the 1965/66 Bundesliga season.
Tasmania Berlin, based in the capital's central district of Neukoelln, now languish in the fifth-tier of German football.
Their chairman Almir Numic - a fan of Schalke's arch rivals Borussia Dortmund - has mixed feelings about potentially losing the record.
"As a Dortmund fan, I wouldn't mind if Schalke continued without a win and even get relegated," he told website Fussball.de
"On the other hand, this story is simply part of the identity of 'Tas'.
"Our only Bundesliga season was five and a half decades ago, but we are still a topic - nationwide. We don't really have to do any advertising."