When the servers start their maintenance, I know that acceleration times are stopped. But what happens with the mines and collectors? Are they still collecting gold/elixir during the maintenance?
There are two answers, because they have two types of maintenance breaks.
Planned Maintenance - this is when they pre-planned the down time for updates, improvements and regular maintenance. For this type, the collectors, mines and drills carry on collecting gold/elixir/dark elixir at a normal rate (boosting pauses).
Emergency maintenance - this is when there is an error/fault/glitch that they are trying to rectify. With this type, they halt everything temporarily so nothing changes from the time the system goes down to the time the system is put back up. It will carry on collecting only after the system is back online.