We are aware of this and have addressed this phenomena over 100 years ago. Rowbotham's original model only contained one celestial and magnetic pole, but after Earth Not a Globe was published the South Pole was discovered and the society revised the Flat Earth model to account for the new evidence. Read the book Zetetic Astronomy by Lady Blount and Albert Smith. The model is also discussed in Albert Smith's The Sea-Earth Globe and its Monstrous Hypothetical Motions.
As for why this hasn't caught on with the wider Flat Earth community, I can only speculate that it is because these later post-ENAG works became available online much later than Earth Not a Globe did and the information has not yet been fully digested and discussed. That first book is so newly online that we don't even have a copy of it in our Library yet, for example.
Thanks for linking the new book. Do you find it to be accurate in its assertions?
I have been a proponent that the earth may have two poles, and we do
speculate in the wiki that there may be two poles. Looking at the old models is interesting. At the moment I am looking at early Flat Earth works on the bipolar model and, while I do agree with the general assertion of two poles, I tend to believe that Lady Blount was wrong with her sun model that depicts two circles, one on top of another, with the sun traveling on one circle around the North Pole for one half of the year and along the other circle around the South Pole for the other half of the year.
Although Samuel Birley Rowbotham is considered the father of modern Flat Earth Theory, before Earth Not a Globe there was a book called
The Anti-Newtonian, written in 1819 an unknown author, which promoted a Flat Earth model with two poles. This is another book that is missing from our library.
Under this model there are two poles, and the sun switches to rotate around each pole for half of the year, but the two circles of the sun's rotation are illustrated to overlap rather than be separate from each other. I tend to like the overlapping sun model illustrated at the beginning of The Anti-Newtonian book over non-overlapping sun model depicted in Zetetic Astronomy. I feel it would bring things closer to observation of daylight and close some questions on the wildly different paths the sun would need to take over the year in Lady Blount's two pole model.