I have been listening to Dr Karl for some time. He occasionally complains about his slide down the scale of trustworthiness in the ABC surveys. Though he is still very credibly in the top 10. I would suggest that this is the reason why:
What the listeners are seeking is unbiased views of the world. They do not necessarily have to be correct, but they should be biased on good science. However Dr Karl occasionally makes the mistake of towing the line of the ABC. So when he gives a view on some topic that is to do with policy he takes the policy line rather than the good science line, even thought they may end up with the same outcome. This makes him a less trustworthy source of information. We do not want dogma, we want honest science.
I have no surveys or other analysis to back up this hypothesis.