What is the ruling on someone who takes a medical treatment that causes excessive urination, leading to the delay of prayer until the time for the next prayer is near?

This continuous urination falls under the ruling of سلس ( سلس البول - urinary incontinence). The correct approach is to delay the two combined prayers until just before the entry of the next one. This is what Imam Ahmad adopted, and it is supported by the hadith (definition) of Hamnah bint Jahsh, where the Prophet, may Allah's prayers and peace be upon him, indicated a suwari (figurative/apparent) combining [of prayers], such that the first prayer is performed at the end of its time and the second at the beginning of its time.