The judgement in the case against Rev Hassan Abduraheem, Christian aid worker Petr Jašek and Dafuri activist Abdulmonem Abdumawla was meant to be given this week but has been postponed until 29 January.
The group was first detained in December 2015 and were charged with crimes against the state. The sentences for some of the charges against them include the death penalty or life imprisonment.
The case against the group centres around the provision of funds for the medical treatment on a man who was injured in a student protest.
A fourth defendant, Rev Kuwa Shamal, was released earlier this month.
A source from Christian Solidarity Worldwide told Premier's News Hour that the men were facing another week of uncertainty over their fate.
"They are having to spend another week in prison - another week of uncertainty of knowing whether the ordeal is over for them so it's really important for us to continue praying for them.
"It's been a very long time that they have been in prison."
The CSW source appealed to Christians to continue praying for the men.
The source said: "We can be praying for the men's spiritual condition and their families who have been on this journey with them. Rev Hassan's family did not even know where he was for the first five months of his incarceration.
"We can be praying for the lawyers who represent the men who have been doing a very good job under very difficult circumstances."
Sudan is ranked 5th on Open Doors World Watch List 2017 for Christian persecution.