Hmm... I don't know exactly what it could be, but could be something to do with memory clearing...maybe somehow the memory isn't being cleared each time you play. Though bit strange this has occured on two cards, so seems more to do with the PC internals.
By any chance could it be overheating? Which is why it might be slowing down?
Could it also by any chance be a driver problem that might have been corrected? Try updating to the latest Catalyst drivers.
You could also check within 'Previous version' to find if anything has been fixed.
If not, memory, or overheating could be the cause of the problem. Though overheating, you'd expect it to be like that after a restart.
Restarting would clear memory though if theres anything wrong with your motherboard slot.
Hope this helps