Even if you know that a requirement is not feasible, be sure not to simply dismiss it away.  Your responsibility as an analyst is to maintain a strong working relationship with the business representatives.  Approach this situation in a way that makes it clear that the decision isn’t a personal one, but that it’s based on a well informed position with associated costs.

Clarify the requirement.  Remember, often when a “requirement” is elicited it is really stated in the form of a solution.  So take the time to verify the true requirement.

Identify why the requirement isn’t feasible.  If the new requirement and the previous requirements cannot be accommodated at the same time regardless of the technical implementation, then present this information to the business.  Do your best to explain the technical limitations using non-technical language that the business can understand.   

Most often however, the implementation of a new requirement isn’t feasible due to the prohibitive cost that would be involved in making the technical changes required to support it.  Estimate the associated cost and present this information to the business.  This is helpful for a few reasons.  First, you may have assumed that the cost outweighed the need for the requirement, but the business may feel differently depending on the business goal driving the requirement.  Second, if the business agrees the cost of implementing the new requirement is just too prohibitive, then you as the analyst have made your case while making the business feel empowered and involved in the decision making process.