Is it permissible to continue an engagement with a young man who has promised marriage but whose current circumstances do not allow it and who asks for space, while feeling reassured about him after performing Istikhara prayer, despite no clear outcome appearing?

It is not permissible for young men and women to get acquainted and communicate, even if it is for the purpose of marriage, because it leads to dire consequences. If the young man asks to end the relationship due to his inability to marry, then the relationship must be cut off, and one should turn their heart away from him and occupy themselves with beneficial deeds. Istikhara (seeking guidance from Allah) is prescribed when contemplating permissible matters to choose what is most suitable.