No, the problem is after 4.6 billion years there should be no comets left. Comets release material continuously. However the "just-so" stories of the scientists try to explain that there has to be a reservoir of comets "that have preserved them in a pristine state" to account for the percentage that we do see still in flight.
You can follow the other links to get the complete logic involved with the scientific model for comets.
The evidence continues to reveal their ignorance, and for some reason has a mounting desire to refute their faulty assumptions.
I think it's funny that you think articles like this reveal the ignorance of scientists, when all it does is reveal the intellectual bankruptcy of the general creationist researcher. Instead of providing viable research of their own, instead they choose to lob insults at the scientific community. Again they show their true colors.
Here's a preprint of the paper that they are crowing about. Maybe you should get a leg up on your creationist buddies, and read about what they think the implications of their work is, instead of relying on a press release. The paper actually reads quite well, especially the introduction(1) and the conclusion(4), and the summary (5), which is all that should really interest you.
Remember that the TNO objects that this paper is looking for is objects of about > 40 km in size. Most comets are 5-10 km in size. They are very undetectable even with the finest current optics. There could be a whole population of them, ground down from larger objects rubbing against each other. Considering how hard it was to image Halley's Comet at the orbit of Neptune, it just gets worse the farther away you get.
Finally, let me end with this statement from the conclusion: "The observed data is consistent with the interpretation that significant mass is present in the CKB (Central Kuiper Belt) and that this mass resides entirely in bodies smaller than ~40 km. It is concievable that, within the standard model of accretion of planetesimals in a (gaseous) circumstellar disk, accretion timescales beyond 50 AU were simply too long for bodies larger than 40 km to form before the present day, or some disruptive event. We note that a substantial mass in D > 3km bodies in an outer Kuiper Belt should be detectable by occultation (of a distant object) surveys in the near future.
At any rate, it should keep the theorists busy for a very long time. The Old Universe theory is far, far, from being dead.