We see that some infants die just after they are born. Some were not born also. Why does that happen?
Like you say later in your own question/post, in general, it is karma. Nothing happens with out the intervention of laws of nature or God.
If the reason of their birth is to experience the karma that they had in the previous
birth, then why are they dying without experiencing their karma?
Experiencing of karma is there in the womb of the mother also, not just after the child comes out of the womb. How the child develops and undergoes pain in the womb is elaborately described by Lord Kapila to His mother Devahuti. See Lord Kapila's instructions here for details.
Will they be re-born again? If so, will they die again like that? What could their previous karma could be? (good or bad).
Laws of karma are complicated. Imagine your java conditional switch/if statement with tons of options based on certain criteria. In some cases the child may just born and die to burn out the last bit of karma and get liberated. In other cases he/she may be born again. For instance if some one is a mother who resorted to abortion she may need to go through same experience by being put in the womb and getting killed. So there is no specific answer, it varies based on a particular situation.
Does that mean that the result that they should get for their previous karma is just dying at the stage of infancy?
In general, yes.
Special cases of karma
Now, in addition to above cases, some of the situations are not just ordinary karma but could be special situations given by Krishna Himself (think of your Java exception handling or intervention of President in the generic government prison operations and granting special alternatives). One who surrenders to Krishna and engages in His bhakti is not under the influence of karma as He says in the Bhagavad Gita 18.66. But we see that those who engage in bhakti also suffer. Is this not like suffering of a typical person who suffers from karma? The answer is no. This is a special situation given by krishna Himself so that the devotee becomes free from all material attachments and can advance further in his devotion, of which liberation is just a by product. This we can understand from His statements in bhagavatam from this verse on wards and other places as well: