Do computers slow down as they age?
No. Most workloads, the processor is what governs performance and the CPU itself remains measurably stable over time in terms of clock rate.



The OS and memory and storage are largely stable. Storage would be the first thing to slow with age, so benchmark that if you can. 

Our expectations of what make for a fast computer however do not slow down. Camera resolution grows, image fidelity grows, more logic is stuffed into a web page, etc...

Software can become corrupt over time, but the computer itself can be returned to factory conditions with an easy erase and install to confirm that the hardware is still speedy even if we don't feel it's so fast compared to all the new young gun computers that are now shipping.



Now from a purely analytical standpoint, here are the items that could conceivably be measured in benchmark or manufacturer tests:


Heat Dissipation failures (thermal grease drying out or dust/worse accumulation) could cause CPU temps to rise when airflow can't remove enough heat from the chipsets. Older CPU didn't throttle as much and had larger metal traces to get the heat out. Newer CPU like the MacBook Air actively reduce cores and clock cycles to thermally control the CPU. This makes for a very noticeable performance dip when the CPU cannot be kept cool. I have seen tower and iMac cases packed with dust or worse / nicotine tar laden dust. So much so, that the computer had no business even running by the looks of it - but other than hot sensors, most still ran full speed (to my great astonishment).
Hard Drive imminent failures - the expected bad block relocation behavior when a drive has to take more time to land data can be noticeable, but I categorize that as your computer has a bad drive - not that it's old and slow. This can happen to a brand new computer with a bad drive until it triggers the SMART status or just fails outright.