I went to the Apple Store yesterday and asked how does the reservation work.
What the Apple employ told me is something I wasn't aware. He said that the reservation system resets every midnight at 00:00 and new stock is placed on the Apple stores across country. The stock that keeps appearing through the day is uncollected reservations being placed back for other people to reserve. If you really want to buy it he said, your best chance is to be up by midnight and reserve it.
And he was right. After having the "This service is unavailable, please try again later" message on the reservation section, it did reset at 00:05 and in a few seconds I placed my reservation. I only checked few stores but it appeared like plenty of stock at that time.