No response Customs systems

Terminal calls late Friday night that a Vessel is loaded and wants to leave, but there is no response from the Customs system. There is no known outage published on the Customs website. Our colleagues at the Terminal have followed the procedure and tried to contact the Customs authorities, but no one answers. Customer is starting to complain and threatens to hold us accountable for demurrage. 

What would be your call on letting the Vessel leave?