It's possible there is some scratch or unreadable area on the original audio CD. Instead of trying to copy the whole CD on the fly, you can use a ripper program such as Exact Audio Copy (EAC) (this is freeware) and it will do its best to copy the digital audio to your hard drive.
By using EAC you can see first if the songs are copied properly. You will not lose any quality--the WAV files are bit by bit duplicates of the data on the CD. EAC will show you the checksum for every song--it lets you test first, and if the CRCs match you know you have an exact read. If the CRC doesn't match you may have a pop or a skip. If there's a scratch on the CD which the drive can't read you will have that. You can try to correct it with an audio editor first.
You will end up with about 40 to 60 megs per song--the songs will be WAV files. Then you can use Nero to create an Audio CD (select Audio CD) and just drag the WAV files in the order you want Nero. It will burn you a normal Audio CD.
PS: you can also compress these WAV files into MP3's which will be 10 times smaller--you can then put 13 hours of music on a CD. But you need to play it on the computer or get one of these widely available portable CD players that play MP3s as well. It will also work on some MP3 capable MP3 players.
Good luck! Hope this helps!