All the mutations you refer to occur at a particular gene for a particular trait so all they can do is vary that trait. If it's rabbit fur color assuming they can produce something new it will be just another fur color. If it's the immune system it will supposedly provide a new protection against a new disease. In other words all such changes occur within the genome, which is the same thing as saying "within the Kind."
But this is untrue. There are not, in fact, genes for "fur colour". If we limit ourselves to the protein coding section of the genome, for simplicity, each gene codes for a protein, and these proteins are enzymes that catalyse particular chemical interactions. So the gene that impacts fur colour does it not by choosing a fur colour but by either altering the pattern of expression or action of other genes, or by catalysing the production of a particular step in a metabolic pathway that leads to the production of a pigment in the hair folicles.
Any change to the protein may produce a different pigment, it may stop functioning at all, or it may produce a substance that does something different. Whatever it does it will alter the chemical pathways of metabolism and may easily produce other effects elsewhere in the animal (few genes actually have a single effect. The multiple impacts of genes are called 'pleiotropy' or 'pleiotropic effects'.
So, in fact, "fur colour" are not simply "fur colour" genes but likely to have other impacts on the organism which are also subject to evolutionary effects and, when they change, they need not remain "fur colour" genes. The same is true for any gene classified by function. Genes operate at a biochemical level where these broad phenotypic traits are not recognisable.
My favourite example of this is the diverse range of proteins that have been co-opted as photoreceptors but whose closest genetic relatives carry out a diverse range of functions in the body. But that are a great many examples, already known about, where the phenotypic effects of genes is highly diverged from even very similar genes.
And evolution, the production of a new phenotype, requires the loss of the genetic material for other phenotypes. That means no matter how many mutations you get the production of a new phenotype means losing all but those that contribute to the new phenotype.
It's certainly true that evolution involves a constant loss of genetic material for other phenotypes. Natural selection is a reductive process, it involves throwing away genes, but the other half of evolution is mutation. And mutation involves not just point mutations but also insertions, deletions, and duplications. This generates not just new genetic patterns but also fresh space for new mutations to occur in.
There is simply no reason to believe that the reduction in genetic diversity should outpace the production of new diversity. In fact, it cannot do so.