You could get around it by discharging the whole load of fuel and reloading fresh, but that isn't good for fuel economy.
Naval reactors do exactly that, but (a) they have very different operating criteria from civil power stations, and (b) they use exotic core designs, with high enrichment and heavy loading of "burnable poison", to get 25+ year refueling intervals.
Continuous fueling greatly simplifies managing power shape and reactivity.