Delaying the prayer from its time can be an excuse for only two things - sleeping and forgetting. Even then, as soon as he wakes up and remembers he has to read it as soon as he can.
However, if other evidence and documents are carefully studied, there will be more excuses.
It is permissible to delay the prayer even if the enemy threatens hard. On the day of ''Khandaq'' the polytheists used to force the Prophet (peace and blessings of Allah be upon hi) to delay the prayer four times.
Also, the midwife and the mother have the excuse when they fear the death of the baby.
There are many other evidences that a person who has not performed the prayer in time must make the qada.
The prayer of qada is done like a regular prayer. If he does qada in the livingplace he prays it completely, if he does qada while traveling he prays it short (qasr). The qada of the witr prayer is also performed.
If a person has not made namaz for up to six times he performs his prayers in order. If it is more than that, the order will be disrupted and he reads as much as possible.
Those who do not know the number of prayers of qada will pray until they think that their debt is over.