In a nutshell:
All fields currently occupied by a country are constanty being resupplied by the factories (truck convoys). Downtime of items like ack, ammo bunkers, fuel tanks, radar, barracks is depending on status of the corresponding factory (resupply by players aside). If the factory is fully up (and the truck convoys get to the field), maximum downtime of those items is 45 minutes.
If a factory gets damaged, this time will increase, when the factory is completely destroyed, the fields will not get any supplies of that kind (and maximum downtime of items on field is extended up to 2 hours).
The factory itself is in turn being resupplied by the city. So you will have maximum effect if you destroy both the enemy city and the factories.