How can a patient with kidney failure combine the Dhuhr and Asr prayers with dialysis sessions that take up most of the day?

Prayer is not waived for a Muslim as long as their mind is sound. If it is possible to delay the treatment session for a short while to pray Dhuhr and Asr combined as jam' taqdim (earlier combination), that is good. Or, as jam' ta'khir (later combination) if you finish before Maghrib with enough time for both prayers and can catch at least one rak'ah of Asr before sunset. If it is not possible, then pray at the appointed time according to your condition: perform wudu' before the session and pray standing. If you are unable, then sitting. If you are unable, then lying on your side (preferably the right side). If you are unable, then lying on your back and gesturing for bowing and prostrating with your head (making your prostration lower). If you are unable, then gesture with your eyes. If you are unable, then recite the adhkar with your tongue. If you are unable, then bring them to mind in your heart. If you wish to combine two prayers for fear of your wudu' breaking, there is no harm, and this is part of the ease of Islam.