Why is it important for a project manager to do stakeholder analysis through out the project?

If you want your project to succeed, with minimal conflicts, you need to get every stakeholder fully "engaged" and motivated .  Engagement and participation instills pride of ownership, leading to better results, delivered in a more productive manner.  The ability to "engage" begins with a full understanding of stakeholder identity and assigned role, vested interest, accountability, and the power to influence resulting outcomes.

To define the relation between different stockholders and set the appropriate communication strategy. 

If you fail to satify any of the stakeholder's optimum needs, he (not everyone) will try to hamper the project by any means.