Frequent Downstream Oxygen Sensor Failures

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My car's Check Engine Light came on a year ago, and the local repair shop replaced the downstream oxygen sensor. That lasted for 3-4 weeks, and the Check Engine Light came back on with same error code again. Since then, my local repair shop has replaced that same Downstream Oxygen Sensor 5-6 times ( all free of charge), with a different brand name Oxygen Sensor each time. But, the problem keeps recurring. Now they have also given up. What could be the source of the problem?