There is no way that an AMD CPU can run slower over time on it's own. The CPU clock frequency is controlled by the motherboard's timing circuit. Something on the motherboard would have to tell the CPU to run slower. Most desktop motherboards don't change the timing of the CPU on their own. However, MSI did make a motherboard that overclocked the CPU automatically at times, but this would not make a PC run slower after several months. So, there is nothing in the CPU that controls it's speed over time and would cause it to run slower after several months. The motherboard's timing circuit will run the CPU at the same speed for the entire life of the PC. Unless of course you go into BIOS and change the frequency manually to run at a different speed, ie. overclocking, etc. But it won't automatically do this on it's own.
The only reason a CPU may slow itself down on it's own is because of heat. I know that P4s have cpu throttling when they overheat, which makes them run slower. If over time the fan on the HSF got dirty and stopped working, then the P4 may throttle performance when it gets very hot and slow down. I'm not 100% sure on how the Athlon 64 thermal protection works, but I think it just shuts the PC off and does not throttle like the P4 does. So, you would never see an AMD processor run slower over time. You could see a P4 run slower over time if it's heat sink fan was dying a slow death and caused the PC to overheat more and more every day and the P4 throttled more and more every day.