This isn't the most serious objection, but it is raised often enough to give us some concern. Many times when someone finds out that I'm highly influenced by Aristotle, especially his metaphysics, it is immediately objected, "his arguments are old." My initial reaction to this is, "yeah, they are old. But, what difference does it make?"
The problem is compounded whenever we consider the many other things we regard as indispensable, but are just as old. I'm thinking in particular of logic and mathematics. I wonder if the person making the objection would also abandon democracy on the ground that it's old. Calculus is getting there, too. In any case, I think the objection is not so much that the arguments of natural theology (and metaphysics, more generally) are old and should therefore be discarded, but that they have been long refuted.
If my impression is correct, then why not simply say they have been refuted? That would save us a lot of time, instead of going over what C.S. Lewis aptly called the fallacy of "chronological snobbery." In addition, most of the alleged "refutations" of these arguments are based on misconceptions, which is what we find in Kant's treatment of the cosmological argument. As for the other cases, I guess I'm just not impressed.