It depends on the settings. If your router frequently saves logs, it will wear it's flash memory faster than if it doesn't save any logs.
For example, the DDWRT 3rd party firmware for the Linksys routers have a feature that logs the traffic. It only writes the log to memory every 24 hours to prevent wearing down the memory too fast.
My routers are over 5 years old and still going strong. But those are out of the ordinary....Today appliances are designed to fail some time after the warranty is over. It's one of the solutions businesses came up with to keep making more money. Gotta keep the economy rolling, right? Someone's got to pay for infinite economic growth.