How can a denied EB-5 case be re-opened?

A motion to reopen must be filed within 30 days of the decision. The USCIS can reopen at any time so you can ask them if there is a legal basis. It has very little chance of success because you should have challenged it at the time.

You may be able to re-apply, but it is too late to appeal or do a Motion to Reopen unless the government based the denial on a regulation which is later thrown out.

You cannot reopen a denied application after 90 days of denial, except when that period is extended to 180 days where denial is due to blatant attorney error. Also, you can file to reopen a case any time after a denial is issued and you did not receive notice from the government. You are then required to move to reopen a case within 90 days of discovering the denial without notice. It seems like you received notice of the denial because you are talking about it. In this kind of case, (EB-5), it may be best to file anew. Whether you file reopen, or you start over, you will need to provide evidence that cures the stated deficiencies in the notice of denial.

Do you know why the case was denied? Is it procedural or was it on the merits? If there was a procedural error, it may be something that can be remedied. If the denial was on the merits, it means the applicant did not qualify. Was your investment returned to you? How much was the investment? Are you prepared to invest in another project?