I have noticed this when running two gnome applets, gnomeicu and gweather. I was also told that this happens with netscape and in that case it problably happens everywhere. If you start the applet (gnomeicu in this case) and connect to the server and then shut down the network and plug in the computer to some other network (with a different nameserver), the applet cannot resolve any names anymore because the old nameserver ip is cached somewhere. You have to restart the applet to get it working again. A bit bothersome when you are using a laptop in different locations.
I've also seen this problem, for the same reason. (Roaming laptop.) This "bug" has been there for at least a couple years, so I'm not sure it's technically a bug. (After all, I can't find anything that suggests that changing resolv.conf will affect running programs.) Regardless, the behavior is very annoying. Only way I know offhand to rectify this is to turn off pump's writes to resolv.conf and install a caching bind. It would be nice if this weren't necessary.
This has been actually discussed on libc-hacker mailing list and was decided that users can use nscd and thus there is no need to add overhead of additional syscall per name resolution (some *stat to check whether resolv.conf was updated). So install nscd and whenever you make changes to resolv.conf, simply /etc/init.d/nscd restart.