Matt, when I suspected copper deficiency I got the vet out to do a blood panel on a mixed aged cross section of all my cattle - weaned calves, yearlings, heifers, older cows. All showed a very marked copper and selenium deficiency despite my land not being copper deficient.
I inject copper, usually annually, and this ensures that each animal gets a dose - mineral blocks or free choice minerals, apart from not supplying the amount of copper required in truely copper deficient animals, are also only as good as what each animal will take and are too hit and miss. Copper can be toxic to stock which are not deficient therefore blocks or free choice are never going to have sufficient copper (or other minerals that can be toxic) in them to correct a deficiency.
Once I started injecting the condition of my stock improved out of sight.
You mention a calf although not it's age. Have you considered BVD? which will show similar symptoms in cattle under 24 months of age - diarrhoea and unthriftiness.
Vets here are not cheap either but I think we probably tend to use them more and in the long term in pays off to know what the health status of your stock is if you have problems that seem to have no reason. Through using vets I know I have a copper and selenium deficiency and supplement them with the result that my stock are in better health, better producing, and grow well. I know I have Neospora in my herd so don't keep any replacement calves from Neospora cows, they get fattened and sent to the works. I know I don't have BVD so only buy in replacement cows or bulls that are certified BVD clear.
Probably a bit more information than you wanted

but hope it helps or gives you something to think about.
Cheers,
Ronnie