I'm under 50, and ride a lot longer distances than you do, but I have found rest days - and even rest months, where I'm riding less, but still riding - to be absolutely critical to both performance and sanity. It is logical: you break down muscle tissue while training, and recovery is the time when it heals itself and the muscle gets stronger.

Unlike when I was running, the only sort of overuse injury I have had cycling I will simply refer to as "a@@ thetans" wherein my sit bones develop an almost funny bone like response to pressure. Those developed twice, both after lots of sustained training and long rides. I backed off a bit, and they left of their own accord.