Philosophically, one could argue that the distinction between organic and inorganic matter is somewhat arbitrary since, at the most fundamental level, everything is simply matter. If you wanted to go in that direction, it would probably be fair to say something like it deteriorated, simply because it's programmed to.

It would also make sense evolution would choose not to change this programming.

Is it destroyed? does matter some how disappear or is it just it transformed from one form to another?

Why did consciousness arise from matter at all, does it disappear or is it transformed.

If you only limit yourself to what you can see then existence is rather dull and seemingly mechanically. Every time we look we see little more, and so is there really anything to suggest there is not more beyond what we can or will ever see.

You mean like our own existence?

There are also species of animals that literally do not age.

The saying that entropy always wins the war is disingenuous as life wins the battles that we can see insofar.

I don't think you need to constrain that question to organic matter. Entropy applies to all forms of information including the information that organizes all known biological life out of mostly water and carbon.