Hello. I have had the same skipping issue for at least five years. About 30-40 minutes into any CD, the music starts glitching -- sounds a little like skipping on a vinyl record, sort of a 'pop' then the music resumes but not exactly where it left off.
I had purchased my BCD-1 new in 2008, so by 2015 or so it was out of warrantee. When the issue started, I contacted Bryston, who have always been very good about servicing their products. (I also own a B60R.) They offered to have a look at it but indicated that if they needed to replace the drive it would cost something like $600 US. At the time, I could not afford to spend that on a CD player repair, so I opted not to send it in.
I found this thread because I started to try to take the player apart, just to see if I could fix it myself, but I did not have the right screw head. Thanks, SilverBullet, for solving that mystery.
Mauvedipstick15, I will be very interested to hear if you are able to find a solution. Sorry that Bryston's initial attempt did not work out.
One other possible solution I discovered was people selling replacement drives online. I have seen one sold from Europe and another from China. It is tempting to order one and see if that might fix the issue. I have very little electronics repair experience, but at this point I might be willing to give it a try.
Hopeful that all of us BCD-1 owners can figure out a solution to the issue.