With conjoint analysis, one rarely tries to throw out attribute levels that are not significant. Before one puts an attribute into a conjoint design, one typically has found from previous research or from expert opinion that the variable has a non-zero influence on choice for at least some of the respondents.
Also, because conjoint analysis designs are typically orthogonal or very near orthogonal, the independent variables have essentially zero correlation among them, meaning that including a non-significant term is less likely to damage the quality of the other parameters in the model than other regression problems in the marketing or social sciences where multicollinearity is a common problem.
Also, be careful that what might seem to be a non-significant attribute level in the aggregate (when pooled across respondents) may actually be highly significant when examining subsets of the data. It's just that different groups of people may feel oppositely about that level (consider brands or colors, for which people can have differences in opinion).
Another issue to think about is that conjoint analysis often involves zero-centered levels within each attributes (the average of the utilities for each attribute are scaled to be zero). That means that for categorical (nominal) attributes some of their levels of middle preference are bound to fall pretty closely around zero. If one conducted a standard T-test to compare some of those middle level parameters to zero, many would likely fail to reject the null hypothesis that the preference did not differ from zero. But this wouldn't mean that this particular attribute level was not a significant driver of choice! You should consider the more extreme levels of a categorical (nominal) attribute (the most positive and negative levels) before concluding with a given confidence level that such an attribute had no effect on choice.
Rather than spend time testing whether attributes have a significant effect in conjoint analysis, researchers typically conduct statistical tests to assess whether one level within an attribute has a higher or lower effect on choice than another level within the same attribute. Or, they compare groups of people to assess whether one group of people thinks that a given level is more preferred (or an attribute is more important) than another group does.