Try downloading the podcast file into a directory then use 'mp3splt' to split it into smaller files.
For example, if you paste this command into a terminal it will download the podcast file into the terminal's present working directory.
The name of the file will be 'vinyltapstreaming_20100403_29816.mp3'
The file can also be taken from the Firefox 'Cache' directory.
The mp3 file is left there after the podcast has been played in Firefox.
But, if the Firefox cache size has been set too small to hold the mp3 file, it could be in the /tmp directory instead and in that case will probably be deleted after it has finished playing in Firefox.
Look for a file of around 24MB.
There are two versions of mp3splt:
mp3splt is a command line tool.
mp3splt-gtk has a graphical user interface.
Both are able to split up a mp3 file into several files without any loss of sound quality.
Screenshot of mp3splt-gtk: http://en.wikipedia.org/wiki/File:Mp3splt-gtk-0.3.png