Not to the extent you are experiencing. You can expect a capacitor with a 3000 hour life (typical for most Japanese capacitors used in the primary) to run for about 6000 hours in a typical PC environment in moderately tropical conditions, without losing any of its capacity. Most electrolytics have a capacitance increase as they age, but lower current handling - both effects due to drying out of the electrolyte. Our long run tests show that high quality capacitors hold up very well, some amps we built ten years ago are still running on their originally used 85C capacitors at very hot internal temps (no fan to help out).
Some power supplies will mistakenly use only load current sensing without accounting for ambient temperature when it comes to operating the fan, this will age the capacitors faster. But of course, it could be just a defective unit. A decently built power supply will hold up fine for over a decade with no drop in ability.