Since the error consistently occurs only at night, it sounds like a signal issue. I doubt that replacing the DVR will make a difference. In case you didn't know, you'll lose all your recorded programs when you swap the DVR for a new one, unless you have a cloud DVR.
Before you replace the DVR, if you're not having to pay for tech visits, I would recommend you contact cox.help@cox.com and ask to have your issue escalated. Request a Cox tech, with proper equipment, test your signal strength. Since the signal to your house can be tested from outside and you work until 6:00 pm, you might ask Cox if you need to be there for that tech visit (if you would be comfortable with that). Also, ask for the ticket number created for your issue to expedite subsequent communication with Cox.
When your issue eventually gets fixed, please post back what was done to fix it.