Try lowering your burning speed to 4x and selecting the "Convert all files to wave" option.
If that doesn't correct the problem, open MP3 CD Burner, click on the File menu and select Preferences. In the CD/DVD Burning preferences, uncheck the "Use IMAPI for burning" option.
If your CD drive is not recognized, click on the File menu, select Preferences and in the General preferences try toggling the "Use Acoustica ASPI" option.
If your version is lower than version 4.12, get the latest version here: http://www.acoustica.com/mp3-cd-burner/download.htm