Why animals can be very intelligent in many areas except for reproduction? I am giving an example to make it clearer. I have a rabbit for some years now. She has learnt a lot of things. She is bonded to me, she can distinguish other persons, she knows approximately the time I will get her out of the cage, she knows not to go in some places, she knows what the direction the doors of the house open so when they are closed she scratches them from that particular side, she can extend her forelimbs to throw down food out of reach, she presses hard food down to crack them better, etc. I think it is pretty impressive for a small brained mammal, and maybe other rabbits can be even more intelligent. But when it came to reproduction her behaivior was more instinctual. I don’t mean that she behaived exactly the same for all aspects of reproduction every time she reproduced, but the core behaiviors would remain the same even if maladaptive. For example if a neonate happened to fall out of the nest, she was unable to put it back again, as her species has no retrieval instinct. If I wasn’t there to put it back, it would die of exposure and she wouldn’t be able to help it. Meanwhile she can more than perfectly carry larger objects than that little rabbit. When she was creating the nest, although in this aspect of reproduction she showed much variation and adaptive behaivior, she still tried to dig the cage bottom even if the little thin substrate had been removed by her, like she was in the soil and digging the burrow. And the effect is similar with most mammals and nonmammals as well. They can be intelligent in their everyday lives, they can learn things to survive better, but when it comes to reproduction, behaivior is mainly invariant. Why? Isn’t flexible behaivior adaptive for the most basic function of life, the continuation of the species?

It's difficult to comment specifically on your rabbit, except to note the general point that parental care in rabbits has not evolved under the selection pressures faced by pet rabbits in captivity. Put another way it is not really reasonable to expect that behaviours seen in captive animals selectively bred for specific human purposes (e.g. floppy ears, docile nature) will fit our (assumed) idea of what would be adaptive in the wild.

However, for your more general contention "when it comes to reproduction, behaivior is mainly invariant. Why? Isn’t flexible behaivior adaptive for the most basic function of life, the continuation of the species?" I would disagree. In fact we know quite a bit about parenting behaviours in the animal world, and one thing we are certain of is that flexibility is common, and often adaptive (i.e. parents alter their behaviours to increase their "fitness"). What is less clear at the moment is how this flexibility (or "plasticity") in repsonse to short term changes in context or environment interacts with the genetic processes teh underpin evolutionary change.

For more info I will (slightly sheepishly..) point you to a recent review article I cowrote:

http://www.sciencemag.org/content/345/6198/776.full

I'm not sure if you can access the full text here or not but if you want it and can't then let me know and I can provide a pdf.

Agreed and would add that there is always a balance between producing large number of offspring and to some extent letting "nature take its course" and a high percentage die vs a much smaller number of offspring which are very carefully cared for and protected by the parents. The drivers for the 2 approaches are fairly obvious and will depend upon environment, availability of food other predators etc.