A reapplication for a COE for the same applicant for the same position is procedurally possible. Whether or not it would be feasible is another question, but there are certainly cases in which a reapplication shortly after a denial is granted.
When a COE application is approved, generally the COE original will be sent by post to whoever it was who made the application, using the pre-stamped return envelope included with the application. When a COE application is denied, the notice of denial will also be sent by post. The notice of denial will have the basic information of the application, the result, and the legal basis for the denial in terms of the immigration law of Japan.
The legal basis and reason for denial written on this notice is relatively general and not very specific to the application. However, it is generally possible to visit the Immigration Bureau in person and request an application at a time specified in the results notification documents. We highly recommend visiting the Immigration Bureau to hear this explanation, because an immigration inspection department worker will sit down and explain in detail why the application was denied.
After listening to the explanation, it generally becomes somewhat clearer whether a reapplication may result in a different outcome. For example, if an application is denied due to insufficient evidence for eligibility, a reapplication in which more evidence is submitted may be successful in some cases, even in filed immediately. However, if the application is denied because an applicant has insufficient years of experience or similar reason, then the likelihood of the result changing is much lower in general. Even in cases where a reapplication approval seems possible, the application will be judged more strictly than others, so the amount of documents and explanations required would likely be higher than usual, and the application inspection much stricter than for most cases.