The reason for the rejection can be found in a letter in the Digital mailbox on My pages island.is.
If the applicant believes that the criteria has changed since the refusal, a new application must be submitted. If the application does not meet the conditions, or if the applicant does not respond within the deadline, the application will be deemed not to meet the required conditions and will be rejected.

Applicants can request a review if they have new information and/or material that they believe will demonstrate that the decision was based on insufficient or incorrect information, or has led to a conclusion that is materially incorrect.
Requests for reviews should be sent by email to hms@hms.is, or submitted via Inquiries and communications on HMS My pages.
The email has to include all arguments believed to have an effect on the outcome of the review and if available, supporting documents.
The matter will then be brought before a committee for a further decision.
Decisions on housing benefits may be referred to the Welfare Appeals Committee.
The deadline for submitting complaints is three months from the date on which HMS announced their decision the decision was announced.