Why is the mishnah concerned just about three days before the holiday and the person thanking his idol for his business with the Jew or offering a sacrifice? Why isn't this a concern all year round?
avraham, Ranaana
Regarding sacrifices it is clear to the Gemara that he doesn't prepare the requirements for the sacrifice for more than three days before the holiday, but of course if he were to sacrifice more frequently this would indeed be a problem.
The Gemara on Daf 7b states (according to the version of the Rishonim and Kisvei Yad) that to do business with a Nochri should also be prohibited since he will go to his place of worship and thank his idol. The same Rishonim (Rashba 2a, and Rosh quoting Rashi) state that the reason we do business with them now is that (a) they are not so devout and do not go to thank their idol after successful business enterprises; (b) if we would not do business with them it could cause friction and enmity and negative repercussions for us.
Other Rishonim (Ritva and Re'ah 2a) state that he only thinks of his idols before the festive days. Other times he does not thank them and does not attribute his success to them.
Some Rishonim (led by Rabeinu Tam) state that the only problem the Gemara has is with materials used for the actual idolatrous practices and not with regular business.
Yoel Domb