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Your old burner cannot handle High Speed CD-RW discs. Such discs have "High Speed" included in the Compact Disc ReWritable logo on their covers, and are usually rated at 4x-10x or 4x-12x, but even 1x-10x indicates an HS disc (since the rated speed exceeds 4x). Although your burner can rewrite at 4x, its laser system doesn't meet the requirements of the newer HS technology.
You should look for CD-RW discs rated at 1x-4x, or older discs rated at 2x. Such discs are gradually disappearing from the market, so in the long run, upgrading your burner may be the only solution.