The Soweto Buccaneers are winless in six matches in all competitions and have scored just one goal in 540 minutes.
After defeating Bloemfontein Celtic in their first league match, they were thrashed by SuperSport United and drew with AmaZulu and Arrows.
Pirates were also eliminated from the CAF Champions League in the preliminary round by newcomers Green Eagles of Zambia, and bundled out of a lucrative domestic knockout competition.
Adding to their woes was the sudden resignation of Serb coach Milutin Sredojevic, who said he was going to visit his seriously ill mother in Belgrade but actually joined Egyptian club Zamalek.
Caretaker coach Rhulani Mokwena, previously the senior assistant to Sredojevic, said it was vital that he and the team "remain patient and do not panic.
"This is the same team that took Mamelodi Sundowns to the wire in the Premiership race last season before finishing runners-up."
"They have not become a bad side in a few weeks -- they are still a good team and one win will change everything," he said.
Pirates had a late chance to win a scrappy match at Orlando Stadium only for a free-kick just outside the box from recent signing Austin Muwowo to be pushed away by goalkeeper Edmore Sibanda.
The scoreless draw left Pirates in the unaccustomed position of 10th, four rounds into the richest league in Africa with a record R15 million first prize up for grabs.
By winning 2-1 at Cape Town City Tuesday, Kaizer Chiefs were assured of retaining first place whatever the outcomes of the six Wednesday matches.
But Bidvest Wits snatched a late 2-1 home victory over promoted Stellenbosch to move within one point of Chiefs and Sundowns won 2-1 at Celtic to lie just two points behind the pacesetters.
South Africa captain Thulani Hlatshwayo scored for Wits and conceded an own goal within two minutes before Gift Motupa netted on 88 minutes to secure maximum points for the home side in Johannesburg.
A Themba Zwane penalty five minutes into the second half gave Sundowns a two-goal lead that was halved three minutes from time when Lesotho international Sera Motebang scored from another spot-kick.