Every person has their own level of endurance even when not training.
When you start the Alternative 100 Push Ups Programme your organism uses that firstAt first the muscles you already carry, will activate. It starts pretty fast and that's why the first couple of weeks are usually easy.
But after these first couple of weeks you'll reach the limit of your current physical abilities. That's when the real development starts... along with the struggle.
Your muscles have to grow and get stronger in order for you to do more push ups – and it takes time and energy. From now on moving on to the next cycle will be more difficult. You will have to repeat some days that you weren't able to do the first time – sometimes you will have to repeat a day a copule of times.
But don't give up. Every time you train, even when you're not able to complete the cycle because you are too exhausted, your muscles grow – you look better and get stronger.
Also, after each solid training your muscles will need time to regenerate and grow. That's why really need the daily breaks.