A water heater that uses a recirculating pump delivers hot water faster than a water heater without one. The pump pushes water through a loop installed throughout the house and allows hot water to be delivered to the fixtures much faster. The upside is that you don’t let a lot of cold water run down the drain, and the downside is that the heated water can give off a lot of its heat during it’s trip throughout the house. The water ends up back in the water heater at a lower temperature than when it left. I’m sure there are studies that say the water heater tends to run more due to this.
Anyway, if you’ve noticed that you are no longer getting near-instant hot water, check the pump. You might be thinking that the pump needs to be replaced, when the problem may be an easy fix. Certainly check to see that the outlet that the pump is plugged into is getting power. If it is not, it may just be a tripped GFI outlet that needs to be reset. The other possibility is that your pump may have a timer on it that is not set correctly. If there was a power outage your pump will be off for the amount of time that the power was out. Resetting the GFI outlet and checking the timer may solve your problem.