One possible flat earth answer is atmospheric refraction. The atmosphere density changes base on where you are on earth which thus changes your perceived star location.
As for a possible FE explanation, being that atmosphere density varies which could cause changing perceived star location wouldn't that make star location variable thereby rendering navigation by which inaccurate?
This is precisely why you need to take multiple readings with a sextant over a period of time and average your calculations for best accuracy. There are atmospheric refraction errors, but they are small. Just on the order of magnitude that requires correction for long voyages, not enough to make navigating by the stars a possibility on the FE. The index of refraction of air is just too darn small for that. By about 3 orders of magnitude.