I read somewhere on the COPA website that within 24 hours of departure you can make a same day change to your flight time if space is available.

Tried to do that by calling reservations this morning and was told I could not change because my booking class (D) was no longer available and I would have to pay the fare difference if I wanted to make the change. They wouldn't even let me downgrade from Business to Economy without paying fare difference.

Is this correct or should I HUCA and hope for a different agent?

You can make SDC on Copa. Fare class does need to be available I believe. However the last time I did it, the same fare class was not available but they put it through anyway. I was CM Silver at the time

D (and I fares, similar idea - restricted version of J/C) fares are a bit or a lot cheaper for a reason - and that is usually no refund, no change unless the same class is available (and which disappear close to the departure date). And the requirement to reprice to what is available is common across all airlines in D/I.

They won't want you to pay for D and ask for the benefits of C. If they did nobody would pay for C at all.

Next time depending on the route C can be not that much worse than D or I fares if that's any consolation. At other times it can be double or triple so it depends on the route and a lot of factors, like if Avianca is flogging better deals on the same routes. Out of Toronto of late Copa's C fares anywhere via PTY were simply crazy. I flew to MGA on Avianca in D for 40% of Copa's C price to the point that even if I dropped the return entirely and bought a new one-way ticket (on AV) back in whatever was available the sum was still less than Copa's fare.