I've only been growing figs in containers for the past couple of years, and only ventured into outdoor planted fig last year with Chicago Hardy Fig which is a cultivar that is sure to survive the winter in my area, but I've been doing a lot of research previously, so here is what I know rom reading, not actual experience --
According to Monrovia's fact page, Kadota figs are hardy to USDA Zone 7 and root hardy to zones 5-6. Which means the top growths will die off if winter temperatures drop to single digits Â°F or below every night for sustained period of time (days), but the roots will remain alive and new shoots will grow in spring from the base of the tree if well mulched and protected from temps in the negative teens.
So it's probably the norm in your location for last year's branches to die off. Kadota can bear fruits on this year's growth and produce mature fruits for fall harvest. So your best bet is to apply a good helping of compost along with the mulch in fall, and another in spring, and probably give it some fruit tree fertilizer in early spring. Keep it well watered but not waterlogged. Hopefully it is planted in full sun (At least 6 hours of direct sunlight) in a well draining spot.
This sounds like an awesomely flavored fig. If I get comfortable with my Chicago Hardy, maybe I will get this variety too....
-- How are you "covering" for the winter? If you can protect it enough to keep some of the previous year's branches, it might fruit on those in spring? Has that ever happened? (We had relatively and abnormally mild winters for a couple of years a couple of years ago....)