First off, make sure the used CD is a CD-RW and not CD-R. Only CD-RW may be written over more than once. Also, make sure the CD-RW is erased before recording over it again. Some burning software will do that for you automatically when you want to burn on it again but some don't and will just recognize that as an already burnt CD.
Sometimes, the CD-RW is just corrupted. I have that happen a ton of times. Some would burn once and could never be burnt on again. Some lose that ability after a couple burns. The best brand I have found is Sony. I still have one Sony CD-RW that has been burnt over at least 15 times to move data from PC to PC. So the brand of the disc does matter also.
As for why your burner will burn but then there is nothing recognized on the disc later that is the software problem. Most likely not the hardware itself. Buy yourself a good burning software or download one for free. CloneDVD is awesome. Here is a link to the shareware which you can use for 14 days.
CloneDVD also gets pass copy protection so you can back up your DVDs. But it's REALLY expensive. Close to $100 USD.
As for CD burning. I like Easy Media Creator although some hate it.
It's also quite expensive close to $100 USD.
But if you buy yourself a very good burning software you won't regret it.
I also use Sonic RecordNow! v.7.2 with my CD/DVD-/+RW and I haven't noticed any problems.
But I did notice the exact problem you had with one of my older CD-RW/R burners running an HP RecordNow! version. Is your burner a supplied burner in an HP PC. Anyhow, upgrade your software to the ones I mentioned and your burning experience should become superior.