Farmville 2 is to our knowledge, the most complex and resource intensive piece of Flash content in common use. It takes a large amount of memory to run -- way more than most other content. It's not abnormal to see Farmville consuming 1-2GB of memory, particularly on a large farm.
On many systems -- particularly systems with 32-bit operating systems or browsers, this means that you're running pretty close to the 2GB per-process memory limit. A 64-bit operating system and browser effectively doesn't have a per-process addressable memory limit (it technically does, but it's absurdly large).
If you're using IE (which is typically 32-bit, unless you've taken pains to run the 64-bit version) or 32-bit Firefox, you might try 64-bit Firefox or Chrome instead. If you've got a lot of open tabs, try closing everything but Farmville. Also, "when in doubt, reboot" is always solid advice.