What format are they being saved in? I'm assuming it will be Windows Media Audio... In which case, you could go into Options>Rip Music tab and see if "copy protect" is selected...if it is, deselect it. Although by far the best method would be to select MP3 as the rip format instead of WMA :)
If you have a decent iRiver I'd definitely recommend having a look at Rockbox [www.rockbox.org], an open source feature rich operating system for your player, instead of the stock iRiver operating system. [although it has the option to load the original system if you so desire]. has things like gapless playback, support for lots more file types [not WMA unfortunately as it does not have an open source decoder] including lossless files, can record to pure .wav instead of mp3, can integrate with last.fm, and best of all: lets you queue up a current playlist rather than having to select a song or album at a time.
... I promise I don't work for those guys :)