This is a common problem with many routers. So much so that many new routers are coming with a centering tool. It's a straight shaft of the size to fit the collet, with a plastic cone that fits tightly on the shaft, but can be slid along the shaft with some effort. You place the shaft into the collet as you would a router bit and secure the collet. Then you slide the cone down the shaft until the narrow end goes through the base plate or router bushing, pushing it to be centered with the shaft and the collet. You then tighten the mounting screws on the base plate or the nut on the router bushing. Make one more check to be sure that everything is still centered and then loosen the collet and remove the centering tool.
Some routers will hold this alignment fairly well during depth adjustments, but other routers require re-centering after each change.