Fission: Nuclear power stations have relatively low capacity factors (a measurement of how much of time they're actually connected to the grid and producing power). This is typically 70% over the last few decades for Western countries (i.e. a third of the time, a nuclear power station is not producing anything). As well as unintended maintenance shut down periods, most reactor designs require a multi-month shut down to refuel. In recent years some countries have managed closer to 90%.

Fusion: By '24/7' you mean the 0.5 s sustained burn at JET in the 90s. Humanity has not yet managed to sustain fusion for a full second on the Earth, let alone get any useful power out of it. ITER (the next generation Tokamak test reactor) isn't built yet. The intent is for it to achieve 1000 s of fusion burn time. Its over budget and behind time, and they've just had a management reshuffle to try and deal with this.

* Edited & extended to try and incorporate nbouscal's feedback from below