I did the math in excel, building a calculator for it in the proces, it's here. Please, anyone else who knows how the math is, go there, and check the math, because if I'm NOT wrong, than this is a colosal overcorrection.
Having watch the siege of Beaumont Spire with interest, I decided to look at the figures.
Damage done per day = 9.2 million
Damage repaired per day = 6.912 million as long as the Base has enough of the 3 Repair Materials.
This figure would be true, if the Server didn't restart once a day and through the couple of crashes that happens.
The Repairs happening during the time the base is taking damage, during the siege time (ships shooting it), will also not count and therefore that 6.912 million hps would be an ideal figure.
Total damage = 2.288
Using a Core 4 as an example, we have:
Figures below represent Day - Start Hps - Hps after the siege is completed - Hps after the ideal 24 hours of Repairs.
1 - 24 - 14.8 - 21.712
2 - 21.712 - 12.512 - 19.424
3 - 19.424 - 10.224 - 17.136
4 - 17.136 - 7.936 - 14.848
5 - 14.848 - 5.648 - 12.56
6 - 12.56 - 3.36 - 10.272
7 - 10.272 - 1.072 - 7.984
8 - 7.984 - DEAD
So the Sieging side only has to win 8 days out of the 14 day siege window.
In reality, it looks like this can be achieved by the 7th day, as the Beaumont Spire was already 2 million HPs behind the curve by day 6 (today).
The other thing noted was that once the Defenders were destroyed (usually in the first 10-15 minutes) the attackers had dealt the day's allowance of damage in less than 30 minutes (with what looked like a handful of ships, unknown composition) and logged off. Thus not allowing the Defenders to come back and try again (if they wanted to).
So for a successful Siege, swamp the Defenders and do the damage, quite easily, before they can come back.
For a successful Defence, kill the attackers and then sit there for the full 2 hours in case they come back, because they can seriously damage the Base in a very short period of time.
The base was also successfully defended once, possibly twice I forget if they defended the second time. Also the attackers lost a days worth of potential damage dealt because the attack window got moved too. Today was if my memory serves me correctly, day 12 of the siege.