Because fusion takes fuel, and the Federation doesn't have resupply depots in the Delta Quadrant.
Technically, it's matter/antimatter annihilation that primarily powers Starships like Voyager. But its besides the point, they both take fuel.
Post-scarcity doesn't mean unlimited resources; indeed, this is prohibited by conservation of energy. It just means that you can always produce enough to meet all demand without the need for competition--and Voyager is cut off from production facilities. Within Federation territory, starships are part of a vast support network. Thousands of light-years away and surrounded by often unfriendly aliens, Voyager had to be much more careful about conserving resources than a typical Federation Starship. They could power the replicators, but chose not to so their fuel would last longer.
We see the reason why Voyager needs to conserve energy demonstrated in the episode where they run out of energy! Running short on deuterium, the matter component of the matter/antimatter reaction that provides the bulk of the ship's energy, Voyager is forced to land on a dangerous planet to refuel. Under normal circumstances, they presumably would have visited a Federation refueling station.
Also you can't (usefully) replicate deuterium, because you'd have to consume deuterium to generate the energy needed for the replication. The second law of thermodynamics: there's no such thing as a free lunch.