At this point I'm pretty much convinced that it needs to be a two-stage thing that is almost identical to the way the ships are setup: first you deplete the shield, and then you deplete the hull. Hull cannot be touched until the shield is gone. Pulse weapons do more shield damage than hull and vice versa, so that multiple ship types are needed to bring it down in one (long) sitting.
The shield is powered by a generator that uses fuel. Attackers hit the shields and knock it down a bit with each hit. If the generator is running, and fuel is available, it restores a fixed amount of shield per cycle. Base owner can turn the generator off to preserve fuel. Size of shield and the regen rate depends on the generator type (same as transport shields). Once the shield is down, the hull is open to damage. Added bonus: solar panel module can regenerate a trivial amount of shield each cycle with no fuel.
Hull repairs... repair crew and supplies I suppose, maybe core size determines regeneration rate, or a specialized repair module. edit: additional hull plating as modules, like with armor upgrade
So this would mean it takes 2x longer than now to bring it down. If the attacker shows up with one ship that is only able to do shield or hull, it will take a lot longer. If they show up with 4 ships that do double damage to shields and hull it will go faster. If the defender is able to run the blockade and bring in fuel, they could extend the life of the shields (and thus the hull) for a little bit, multiple suppliers could stretch it out indefinitely.
edit: also need to calculate time-to-die based on possible damage. EG, heavy mortar does 500k damage, so how many million hull hit-points to make it survive 2 hours with default regen times?