What is the ruling of Islamic law on the engagement remaining for a long period after the marriage contract, with recurring problems due to the delay in marriage and the girl not completing her studies, and her family's refusal to expedite the marriage?

This action goes against the Prophet's command (peace be upon him) who encouraged marriage to those whose religion and character you are pleased with. It also leads to missing out on great benefits such as chastity and righteous offspring. It is possible to combine marriage and study, and if they conflict, marriage should be prioritized due to the tremendous benefits it entails. One must also be wary of mixed-gender education and immodest environments.