Adding coefficients makes P value of a regression go down. Why?

Hello. I'm reading through an example in a book that runs a regression showing that sales of eggs decline with increasing prices. The standard deviation of the slope is far away from zero and thus has a very low p value. However, when we create additional coefficients (pre-Easter, during Easter, after Easter) the values of the added coefficients are significant but the original coefficient (which now is non-easter sales) is no longer significant. What does this mean and how can it be? Thanks.