Changing mp3s to CBR doesn't remove skipping?

I've had two CDs recently converted to mp3s give me trouble when played on my iPod. In both cases, the songs would play part way through and then skip to the next song. Research here and in other forums suggested I create Constant Bit Rate mp3s to avoid placing a processing load on the iPod's relatively small "brain" (whereas most mp3s are Variable Bit Rate and the device playing them has to follow that variability during playback).

This worked great on CD of blues music. However, it's not working with the CD of classical guitar. The CBR mp3s in that second case will skip during the song or even not play at all and skip to the next song. I've tried one suggestion of looking at the file in iTunes and making sure the beginning/end were defined as the actual full length of the song. No luck. Any tips?