This maybe due to copy protection on the CDs. Are you trying to rip it on a Windows machine or a Mac? A Mac may have more success. Also try using a different program other than iTunes for Windows to do the ripping of the CD and then afterwards import the resulting files in to iTunes. You can still use an external USB CD drive on a Mac. Even if these particular CDs are not protected a previously inserted and copy protected CD may have installed software in to your Windows PC to sabotage future ripping, this effectively malware does not exist on Macs hence my suggestion to use a Mac instead. Sony have been particularly guilty of dirty tricks like this.
With regards to alternative CD ripping software - for Windows many people use EAC (Exact Audio Copy), for Mac the nearest equivalent is XLD which can not only convert between lossless formats like FLAC, AIFF, WAV and ALAC but also rip directly from CD with error correction like EAC.
The best format to use would be ALAC and it is possible to install a plugin for EAC to let it use this format, XLD supports ALAC as standard. (ALAC is Apple Lossless Audio Codec.)
Note: As proper genuine 'RedBook' audio CDs have no copy protection it is generally considered legal to rip your own purchased and owned CDs. This differs to the situation with DVDs and Blu-Ray.