COE cannot be re-issued even if it is lost or stained. In this case, application for issuance of COE has to be made again.
As a side note, the applicant can file the document called "Request for Document Diversion" when applying again for issuance of COE. This document is for requesting Immigration Bureau to consider the documents that have been filed in the previous application as the ones filed for the re-application. With this system, applicant can save the saves the time of preparing the required documents again for the re-application.