Personally, I find CR to be much better than CS, at least when dealing with problems. So very many times the first response from CS is way off the mark and I end up having to reply with a very long explanation (the web being limited to 1500 characters just doesn't do it many times). An example is writing them about a problem with a window seat and the first response goes into details on how to use the window shade.
As to your specific point, AA does record many calls. However, if you can get back to the actual CS rep, they may remember the transaction and facilitate a refund. Unfortunately, if the AAgents rolled over every time someone claimed a loss, AA would not be in bankruptcy but defunct!
Good luck getting this resolved.