I understand your frustration, but as i said, i can't think of anything on the Openfire side doing this on purpose. I was mad when after upgrading to 3.9.3 Openfire couldn't run half a day without running out of memory and halting. Then i have installed it on Windows Server box (was Arch linux) with the current Java 8 (was old Java 7) and it runs smoothly now. Not sure what was the cause. You should check Openfire logs. Maybe you will find Out of Memory errors there.
Also to clarify. Are you running one central server and all users from all the sites are connecting to this one server? And when 4 users from the affected site can't login, what about the others? If they still can login, then i would think it is something on the network side of that site.