What are the permissible excuses for making up prayers? May Allah reward you.

The question is unclear, because making up prayers is obligatory when its cause exists. Every Muslim who misses a prayer must make it up, by scholarly consensus, if it was missed due to an excuse like sleep or forgetfulness. Similarly, if one intentionally abstained from it, according to the majority of jurists. As for delaying a prayer beyond its prescribed time, it is not permissible unless it is one of the prayers that can be combined by delaying (Dhuhr and Asr, Maghrib and Isha), but this combining has valid excuses that permit it.