Language is a living entity which evolves with the mood of the people as much as to any rigid
 formula, so there may be no straight answer.
However, here are some explanatory factors, in decreasing order of importance:
1) Contraction is rarer than possession, in general, so needs to be stressed more by retaining the
 apostrophe.
2) "it's" (pre-poss.) is shorter than "it is" (pre-cont.) so "its" (poss.) needs to be shorter
than "it's" (cont.).
3) he, she already have peculiar possesssives (his/her) encouraging same for it.
4) Contraction combines both "it is" and "it has" -> "it's", so standard usage is right 2 out of 3
(rather than reverse usage right only 1 out of 3).
5) Contraction for this specific case ("it") is the more common occurence, so should be given
 precedence