The club from Mediterranean city Sfax, 270 kilometres south-east of capital Tunis, have made a poor start to Group B, losing away to Egyptians Zamalek and drawing at home to Congolese AC Leopards.
And one point from a possible six means a share of bottom place in the mini-league with Leopards, five points adrift of Zamalek and two behind Pirates.
In the three Confederation Cup-winning campaigns, Sfaxien collected six points once and four points twice from the opening two group games
Duarte, 46, arrived in Sfax this year after making little impression as coach of Gabon and Burkina Faso.
The Portuguese has clashed with Sfaxien officials, accusing them of "falling asleep" during the transfer season and leaving him short of talent and depth.
There has been unhappiness among players, too, with Mohamed Ali Moncer pondering whether to renew his contract while fellow attacker Taha Yassine Khenissi wants to leave.
Better news for Duarte is that captain Ali Maaloul, who equalised from the penalty spot against Leopards, has signed a two-year extension.
Former CAF Champions League holders Pirates started with an away win at Leopards, then slumped at home to Zamalek, winners of nine African titles.
Defender Siyabonga Sangweni is available after an injury and coach Eric Tinkler may consider starting with Lehlohonolo Majoro after he came off the bench and scored a superb goal against Zamalek.
“After losing to Zamalek, it is important that we do not suffer a similar fate in Tunisia,” stressed former South Africa midfield enforcer Tinkler.
Zamalek host Leopards in Cairo and will be confident of success having trounced the Congolese 4-1 in a Champions League group game two years ago.
The Egyptians have improved considerably since while Leopards have not built significantly on the promise created by winning the 2012 Confederation Cup.
Bassem Morsi, Mostafa Fathy and Nigerian Maarouf Youssef are among the talented young Zamalek attackers Leopards must contain.
Egyptians Al Ahly, the Confederation Cup title-holders and winners of a record 19 CAF competitions, have home advantage over Tunisians Etoile Sahel in a top-of-the-table Group A showdown.
Etoile have six points and Ahly four ahead of a match in Suez that could hinge on how successfully the visitors contain Ahly star Abdalla Said, who bagged a brace during a matchday 1 rout of Tunisians Esperance.
Having lost twice, Esperance must collect maximum points at home against fellow strugglers Malians Stade Malien to retain any chance of a top-two finish and a semi-finals slot.
25.07.2015 19H00 Al Ahly (Egypt) vs Etoile du Sahel (Tunisia)
25.07.2015 19H45 Esperance (Egypt) vs Stade Malien (Mali)
26.07.2015 19H30 Zamalek (Egypt) vs AC Leopards (Congo)
26.07.2015 20H30 CS Sfaxien (Tunisia) vs Orlando Pirates (South Africa)
*All times are in local time