Typically the operators will have an agreement so that they can get the generators refueled should the outage last even longer than what fuel they have on premise, so they theoretically could run indefinitely on generator power.
At the 1wk+ territory, it will start to look something like Katrina, where the roads were all blocked by flooding waters and fuel resupply missions required the protection of the National Guard.
I mean you can charter helicopters to bring in fuel, but I think there are more urgent things to power than a datacentre in those cases, for example, hospitals and shelters for emergency humanitarian aid.
The DR/BC space has become pretty robust, and with the right vendor, a datacenter loss can be recovered from simply by powering on fully-replicated VMs in another datacenter.
http://www.wsj.com/articles/SB100014240529702047893045780871...
Edit: One of my fond memories of that time was actually greeting the refuelling truck and directing it to the point where he could plug a hose into a pipe on our building and start pumping.
[1] https://en.wikipedia.org/wiki/Northeast_blackout_of_2003
This reminds me of a blog that was live-updated during Katrina by a data center operator: [1]. They managed to keep everything running through the whole storm, IIRC, but it was pretty dicey -- moving barrels of diesel by hand, staying on-site and surviving with water rationing, losing all but one upstream fiber, etc. Fascinating reading in hindsight.