A similar thread was on Alla recently, so I'll just post my reply from there:

Something I've found in some schools of programming is that time is measured in seconds from a specific point, 19:00 EST on Dec 31 1969. Each second that ticks past this date is added onto the counter. Now, if you perhaps unlocked Abyssea on June 03, 2010 at 5pm exactly, 1,275,598,800 seconds would have passed from that time. This number will become your starting point for the stone refresh.

By default, we know the starting refresh time comes in 20 hour increments (72,000 seconds), possibly enhanced to 8 hours (28,800 seconds) depending on your abyssites. This number isn't important just yet, though. The first check the game will go through is to subtract your start time from the current. So, using the above and 00:00:00 Mar 15 2011 (1,300,161,600 seconds), we find that 24,562,800 seconds have passed.

Now that we have that number, we take your refresh rate and divide the seconds into that.

20h: 341.15
16h: 427.437
12h: 568.583
08h: 852.875

Since we can't have fractions of a stone, more than likely just truncates it off. Anyway, you then take the numbers harvested above and subtract the amount of stones you've spent. This will give you your current total. This is also why people who were sitting at almost no stones wouldn't see their supply increase much after getting one of the abyssites.

Overall, SE's chosen start date doesn't matter much (It could be 00:00:00 Jan 01 2000 for all I know), but it's probably tied into the seed for their random number generator. Regardless, seconds are always passing and it's more than likely that whenever the servers come back up, you will have more stones. I'm doubtful they'll have paused auctions or gardening, as they more than likely also have time stamp checks that are processed with every game tick.
Additionally, stones still accumulated when servers were otherwise down for maintenance and updates. Don't worry about it. Enjoy however many you get once the servers are back up.