I had this same problem with my iMac G5. I called applecare and it turns out that it is a problem with the drive. Or that is what the applecare tech person told me. I ended up having them send me a new drive and I put it in myself. Since then everything has been good. I have not tested it tough but of the burning I have done i have not gotten the error again.
Hopefully you have applecare on the mini!! If that fails you can always buy a different drive and install a new one yourself. Riskier but it can be done.