Thank you all guys,
Indeed, the problem occurs with Chrome and IE, and not with Firefox - as I said.
In most hours of the day it works, so the problem has probably something to do with a scheduled task.
Every day it stops working on 03:00 AM and starts working again at 10:00 AM (New York Time). Every day!
It's probably related to some scheduler, right? How can I locate such a scheduler?