During the day of black sun it is shown that all firebenders collectively lose their bending during an eclipse. in both the fire nation and omashu it is the same.
HOWEVER
eclipses don't work like that.
The assumption is because the sun is entirely blocked out for 8 minutes, firebender's power gets so weak to the point where it is non-existent. there are already problems with that.
This assumes that sunlight gives firebender's power. which would also mean they would be just as if not more powerless at night, but thats not the case.
The only way to mitigate that logically is to assume that the sunlight reflected at night allows firebending.
But here's the problem
Eclipses, at least in our world, only block out a specific part of the planet because of the size of the moon in proportion to the sun. this area is actually quite small compared to the earth itself.
This would mean it would only shut off for people in a certain area, not the globe.
On top of that, omashu and the capital are very VERY, far apart. if we're using the map for reference, they would actually be on near-opposite sides of the planet, meaning it would be the middle of the night in omashu during the eclipse on the other side of world.
Then, coming back to the day-night problem. during the lunar eclipse (when zhao killed the moon spirit and literally destroyed the moon) the firebenders should have also lost their power if we're going with the assumption that firebenders can bend at night due to the reflection of the light from the sun.
This is the problem with staking the power system on celestial bodies, because they have to adhere to celestial patterns and conditions. it wouldn't be a problem or as confusing if firebenders didn't completely lose their bending when sunlight is block out.