Helping people with computers... one answer at a time.
We'll look at why you might not be able to add files to a CD-R.
Burning CD-ROMs has gotten easier over time, but it still suffers from some obscure terminology and odd situations. Add to that CD-RW (which is quite different from CD-R), and I can easily understand some confusion resulting.
It depends a lot on the tool you're using to burn your CD-R. I happen to use Roxio's Easy CD Creator, but I've heard good things about Nero as well.
You stumbled on to one of the key terms: closed, sometimes also referred to as "finalized". When you burn a CD-R you can elect to leave it "open" - meaning that more files can be added to it. Often case the default is to "close" the disk, meaning as you've seen, that no more files can be added.
When you leave the CD-R open for more files, the disk space is used slightly less efficiently, and there can be occasional glitches. In researching this article I burned a CD-R in two sessions; I burned a set of files and left the disc "open", and then added another set of files and closed it. In a command prompt it correctly shows that the disk now has around 650 megabytes on it, however Windows Explorer shows it as having only 298, the size of one of the two sessions. All the files are visible in both cases.
My approach to burning CDs has always been to collect up "around" 650-700 megabytes of stuff, and then burn the entire disk in one sitting - closing, or finalizing it. I believe that's the safest, most compatible approach. Multi-session CD-R support was added after CD-R's had started to become popular, and while it works and is convenient, there's still a slight risk that the CD-R might not be readable on all PCs.
And to be clear, CD-R is what's called a "write-once" technology. Once you write to it, you cannot erase what's been written. CD-RW is a Read/Write technology, meaning that you can write, and erase from the media. CD-RW uses a different type of media.