It is always helpfull to know if your animal is wild caught or captive bred. There are tonnes of CB copperheads available, but there are probably an equal number of wild caught animals taken in as well.
Inappetence is a pretty non-descript sign. Begin with reassessing your husbandry. The most common culprit is inadequate temperature, but this is not the only reason a snake may not want to eat. Go to the venomous forum for more specific copperhead care.
The fact that your snake has tried taking mice and then rejected them may shed a bit more light on the situation. If your snake fully swallowed the prey, and then later regurgitated it, this is more indicative of a systemic problem, such as inadequate husbandry, septicema, toxicity, organ failure, stress, ect. in no particular order. If the prey hasn't passed passed the head, it may be more likely related to a pain response whether it is an oral abscess, trauma, or esophageal injury.
My best course of action (in addition to close monitoring, and weight records) is to verify the husbandry is correct and improve upon in any way possible. Don't offer food for 10 days, but keep plenty of fresh water available. Offer a smaller than normal prey animal. If no success, and/or other symptoms arise (like a swelling, coughing, wheezing, lethargy, bleeding, soft stool.. ect)then having your snake examined by a "hot herp" vet is necessary.
If you do not yet have one check our www.arav.com
Good luck with your copperhead
Ian