Providing your other backups other than these from the current batch of discs you are using work fine then you can rule out the PS2.
If all your other discs are doing the same then you can blame the PS2.
Try another pack of discs from a manufacturer you know work well, e.g. Ritek G04. If this solves the problem then it was a bad batch of discs / poor media.
If the new discs still don't do the trick, but the PS2 is fine with your older backups, then it could be that your DVD-RW Drive is knackered...
It's just a case of following this and ruling out what isn't causing the issue leaving the one that is
Good luck...
LUFCfan