At first the site was getting slow and going down. The host identify a bunch of IPs that were sending massive number of requests to the site so that seems like a DDoS attempt.
During the chat (see chat transcript) access to the site was regained and all the access apart for strictly selected IPs was closed.
A number of security precautions were taken and the site was back open for access. It goes down immediately now. Server logs show continuous access attempts that looks like port-scanning. What else can be done?