Why does this happen every day at 3PM?
Backups get taken daily - and the database is now so large that the site stops responding for a few minutes until it completes.
The time was chosen to be approximately the low point of daily traffic on the site.
The following chart shows the number of sessions (visits) for each hour of the day, with times in GMT:
You'll see that the quietest time of the day is approximately 5AM GMT, which is 15:00 (aka 3PM) on the east coast of Australia.
So as annoying as it is for it to be unavailable in the middle of the day here in Australia - I figured it was the least disruptive time of the day overall when we consider the international audience of the site.

