Cox will probably bill you for replacing that box and it's not likely to fix the error. An equipment issue that only occurs in the evening hours seems unlikely. The equipment issue you're describing seems unlikely anytime. Cables may need to be replaced, but the box on the side of the house shouldn't need to be replaced unless it's damaged.
A main line signal issue is still the most likely cause of your error. They often only occur during peak usage hours and would explain the issue you've had with your remote not working. The neighbor you spoke with may not be on the same node with you. Before scheduling a tech to replace equipment, check with the neighbor on the other side of your house to see if they've had a similar issue.