Why do people not answer amen to the blessing over fire in havdalah in shul, even when they answer amne to all the other blessings of havdalah?

Shalom, The practice you write of - not answering amen to the blessing over the fire during havdalah in shul - is one that I have never heard of, nor seen. After searching through many halachic works I am still unable to give you a clear explanation. If this is an established practice in your shule, may I suggest that you ask the Rabbi of the shule for its source. If, however, there is no source - or there is no Rabbi in the shule to guide you otherwise - then I can tell you that the correct practice is indeed to answer "amen". In certain cases, one should not answer amen during havdalah - but this is only if you intend to drink the havdalah wine yourself, and rely on the blessing for wine said during havdalah. Even then, if you are fulfilling the mitzvah of the candle or spices during havdalah and relying on the Chazan's blessings, you should answer amen to the Chazan's blessing. (See Shmirat Shabbat KeHilchatah 60:27, and 61:8). Blessings.