I usually set and recommend a country mirrors pool to avoid this.
Nevertheless, on help threads on the French forum, I often see users who set a specific mirror, trying to optimize speed.
When checking https://launchpad.net/ubuntu/+archivemirrors I observe that "up to date" is not the majority and that some lag up to one week
Why is this? Isn't the mirroring process automated?
The answer is "It Depends on the Mirror and Its Configuration".
Mirrors are able to sync in more than one way. Typically, they rsync data over more than once a day, but sometimes less than that if they are limited on bandwidth. There is a mirror "push" process which can rsync data to the mirror as it is made available in the repositories, but this can be bandwidth intensive.
As a result, because syncs may not happen in a timely manner on the various mirrors, they can be out of sync for various time periods.
Note that not all mirrors are run by Canonical - they run the official Repository servers and mirrors, but not necessarily the rest of the mirrors on that list. There are a number of mirrors set up by various companies that're on the mirrors list who have asked to be on the list, and it's up to those individual mirror providers to have the proper sync systems set up to sync up in a timely manner.