That's a really question that had never occurred to me before. Fortunately it had occurred to Dr. Joseph Kunkel, who is a professor at the University of Massachusetts. He has a webpage listing pretty much everything you would want to know about cockroaches:

bio.mass

Dr. Kunkel's answer to your question has to do with the way radiation actually kills things: it damages DNA. Apparently cells are most sensitive to having their DNA damaged by radiation when they are in the process of dividing. This is why radiation is used to treat tumors. Tumor cells are dividing rapidly, so they are more sensitive to radiation than the non-tumor cells surrounding them. Radiation will damage the DNA of non-dividing cells, too, but those cells can often repair the damage before it is time for them to divide.OK, so radiation is especially bad for dividing cells. Humans (and most other vertebrates) have lots of cells that are dividing all the time, especially in the bone marrow where blood cells are made. These cells get zapped when humans are exposed to radiation, which is why victims of nuclear accidents often die of bone marrow diseases. But cockroaches (and insects in general) only go through cell division every once in a while. Insect cells divide right before the insect molts its exoskeleton, but otherwise the cells aren't dividing at all. So if you pick up a random cockroach and expose it to radiation, chances are none of its cells are dividing and it will survive the radiation. If lots of cockroaches get irradiated, the ones that die are probably the ones that were undergoing cell division at the time. This isn't just true for cockroaches -- a number of different insect species have been exposed to radiation in the lab, and they all had very high survival rates.

Unfortunately for cockroaches, but fortunately for the Orkin pest-control man, cockroaches don't have a similar advantage when it comes to pesticide. A lot of the pesticides used on cockroaches are neurotoxic, meaning they interfere with the transmission of nerve impulses. Cockroaches might not undergo cell division very often, but like all animals they are constantly using their nervous system. So when pesticides inhibit their nervous system, they die fairly quickly. Thanks for asking an interesting question!

Even though cockroaches sound invincible, there is no such thing as a "super-organism" which is immune to all toxins. Insecticides work because scientists have carefully formulated these pesticides to cause damage to roaches in particular. For example, some insecticides are called "growth regulators," because scientists have created them to interfere with the cockroach hormones which control molting. Basically, these insecticides prevent roaches from turning into adults; therefore, they can't breed and produce new roaches. Because there are a number of different roach species, scientists have had to determine the best way to kill each different species. See the UC IPM website for more information:

pestnotes

Some scientists think that roaches may be able to survive extreme radiation because their cells divide less rapidly than humans, so they are less susceptible to cancer. However, some scientists think that roaches are just as vulnerable to radiation as humans are. See the paragraph at the bottom of this webpage for more details:howstuffworks

It does seem odd that a little spray from a can could cause more damage than radiation. Actually cockroaches are hurt by radiation; it just takes more of it.

Pest sprays often target particular chemicals, called enzymes that are vital to life. All living things need enzymes, but not exactly the same ones. For example, some pesticides attack the enzymes that help insects maintain their "shells" or exoskeletons. Since we don't have exoskeletons, these don't bother us much. (We have endoskeletons. Exo=outside, endo=inside.)

Radiation poisoning happens because the DNA in our cells gets messed up.All living things have DNA, but some animals are more protected from radiation than others. Animals with cells that are dividing are the most likely to be hurt by radiation poisoning. Every time cells divide, their DNA has to be copied and divided equally into the new cells. Most of our cells do this all our lives. Cockroaches have very few dividing cells after they are adults, so they aren't as easy to hurt with radiation.

The lining of our gut is being constantly replaced. Our brain cells almost never divide. Why do you think some cells divide more than others?

I wonder if having an exoskeleton also gives them some protection. You gave me something interesting to think about.