I have a Sony CD player / copier of a similar vintage, also designed when CD-R was relatively new. It has proven to be very sensitive to the brand/type of CD-R media used in it for copying and playback.
One issue I've noted is that it will not play or record onto what it thinks are "data CD's," which seem to be anything of the 74 minute variety. It accepts the 80 minute "Music CD" format much more readily, but even within that, it seems finicky. Sony Music CD-R's, somewhat unsurprisingly but aggravatingly, work fine, though are more expensive than other brands and types.
I don't use it much any more, but when there were two cars and drivers in the household, I would often want to make a copy of a new music CD for each car. The machine would usually make one copy, and then, with no warning, it would blithely make coasters thereafter, even on the media it seemed to prefer. I suspected this was some kind of Serial Copy Management System issue (Sony was also in the music business then), but was never sure about it.
Nowadays, it's rare that I use it, and it may soon find its way to Goodwill. Anyway, you may find that your machine has some preferred media that works well while others are unpredictable. That has certainly been true for this machine and another one or two of similar vintage I've used over the years.
