Refueling and maintenance are the "normal" things and both are planned to the time of year with least consumption/lowest electricity prices.

Then you have the rare non planned outages but once a new reactor has been running for a year or two and all the kinks have been worked out they should be very rare.

Not an expert, but it's my impression that it's common to have reactors shut down about one month per year for refueling and maintenance. Of course, this can be planned so it's not a big deal.

The plants do have a worse correlated failure mode which is when something bad is discovered in one plant, it can shut down multiple plants because the safety is based on making sure to an extremely high degree that nothing can go wrong - like grounded air planes. Something like Fukushima can shut down plants all over the world temporarily until plans have been revisited and extra precautions possibly put in place.

Scheduled maintenance. Refueling, replacing worn-out components, that sort of thing. One nine of uptime is pretty good in the "continuously running power plants" business.

Emphasis on scheduled. Wind operators get no choice at all in when they're generating power, and this is true of solar as well, although the fluctuation is easier to predict, especially in very sunny climates.

A fleet of nuclear reactors can be taken offline on a schedule, with advance notice, so they alternate being out of commission. This makes it easier to supply reliable baseline power.

Nuclear plants, like any facility or service, need downtime for maintenance

Over their lifecycle they are down more like 20-25%.