InstallationStatus = 3 does indeed mean licence expired.
The date format won't affect the evaluation of the date. The only way that the licence will get that status is if the current date falls outside the validity period of the licence (ie. StartDate to EndDate); or in the case of indefinite licences, when the current date is earlier than the licence start date.
It's curious that it worked correctly the next day. Could any of the dates have been changed in Licence Master admin, or could the licensee have made a mistake entering the licence number?
A few questions to help narrow this down:
Did the licensee provide you with a screenshot of the error message they received from your module? How did you find out that that was the status they received?
As the actual message displayed in response to the status is decided by the client application, have you checked that your module displays an appropriate message for the LicenceExpired status?