To begin with, there is no rule that commands a species to mutate and produce some new species. There are loads of species that have been around, unchanged, for millions of years. And of course, bacteria are still with us in great abundance. They haven't all developed into multi-cellular creatures. A new species probably won't happen unless a mutant group is separated from the parent stock, or if some disaster kills off the parent stock, etc. In the absence of something like that, all you'd have is a species with a lot of genetic variation in the population. But that variation is the potential for speciation if conditions warrant.
As for some species now going through the process, how in the world would you recognize it if you saw it? Are penguins on the way, millions of years hence, to becoming something else? What's to become of the ostritch? How about those "walking catfish" you sometimes read about? How many species of birds are there? Or beetles? And how many more will there be in 100,000 years? As I said, every species has the potential to produce mutated offspring. Some will eventually produce a new species, some won't. These things take time. From the fossil record, we can see that it's happened. There's no reason to assume that it has stopped. (Except perhaps in our own case, as it's very easy now for virtually every individual to survive and breed.)
I am sure that you would disagree but the above paragraph has the same reliance on "faith" and was written with the same religious fervor that a creatiionist exhibits when confronted with a question for which there is NO answer...yet. Fossil records are a very un-focused snapshot of the past in very specific locations and even those that are responsible for interpreting them admit that they come to conclusions based on assumptions that are being revised daily. I am not saying they are wrong, I am saying that those MOST educated in modern evolution do NOT take the absolutist positions of those laymen that have embraced the concept as an alternate religion. I am not arguing the traditional creationist position, I am looking at the gaps in both and see that MANY of those gaps could be the result of blind-spots and personal bias on both sides of the debate.