You may have had two defective DVRs, but your symptoms also occur with a weak signal. If that's the cause, there may not have been anything wrong with either DVR. Have you had a tech check your signal since the issue started a year ago? You should do that before swapping another DVR and losing recordings again since a new box might not solve your issue.
If you don't have Cox Complete Care, you might consider subscribing ($10/month). If Cox doesn't find an issue with their signal or equipment, they'll charge you $75 for a tech visit that would be covered by CCC. You can cancel after 90 days. It you cancel earlier, Cox will bill for the tech visit.