There is a certain magic in the number 3. It doesn't take much thinking to think of the trinities of various religions of which there are the 3 main gods, usually, it is the Father, the Son, and a female representation that we can call of Mother.
I totally agree with you the number 3 is a universal number and it stands for good fortune maybe because 3 stands for trinity.
After 3 disappointments, we will hardly suffer a fourth with the same person, and even if we suffer, it will certainly not be the same way as before, we will certainly be wiser and more prepared.
Things get better after 3 trials because we must have learnt from our past mistakes and even worked on our weaknesses.
Then taken corrective measures.