The last season's runners-up slumped to a 3-1 defeat to Petrojet before being held to a 1-1 draw by Arab Contractors to dent their chances of winning the league title for the first time since 2002.
They are eight points behind bitter rivals and league leaders Ahli, who played a game more.
"The upcoming games will be difficult, but we will not give up," Soliman, whose job is reportedly on the line although Ismaili gave him a vote of confidence, told FilGoal.com.
"I did not promise the fans that Ismaili will win the league this season, but we are in a position to mount a serious challenge at the top."
Soliman took over at the team in August last year following the sacking of Serbian coach Nebojsa Vuckovic, who was shown the door after the team's first two league games.
The Dervishes struggled for consistency and hardly filled the void left by the departure of Iraqi striker Mostafa Karim and the injury of attacking midfielder Omar Gamal.
Their defense has also been shaky, with trio Ayman Ramadan, Ahmed Hegazi and Abdul-Hamid Sami failing to deliver assured displays at the back.
Speculation is rife that Soliman will be sacked if Ismaili stumble again when the league resumes following the international break.
"In 17 games under my guidance, Ismaili lost just once. This is good," Soliman added.
"There were rumors that the board intends to dismiss me, but this is totally untrue. My job is safe."