I'm sure there are shareware-type downloaders out there that would work, but money doesn't grow on trees for a lot of us folks. So I use the built-in curl command in Terminal. Trying curl in Terminal using the options -C - -O will work for most sites. However, for sites (like MacObserver) that are using a service such as CacheFly which uses redirects, it won't work. I was stumped until I contacted CacheFly, and they pointed out that "you can have curl follow redirects by passing it the -L flag."
I had read the help for curl, but did not understand what Follow Location: hints (H) meant. Finally! Now I can grab the podcast URL from the website, and then run this command in Terminal:
curl -L -C - -O http://url.of.podcast
Even if the connection gets killed before I've finished downloading (hours later), I can resume and finish it. I hope this helps at least one other dialup user out there. Hopefully Apple will eventually connect iTunes with tools like curl that ship with OS X to upgrade their download capabilities.

