They look to be doing the load balancing via F5 BIG-IP. They're pretty much an industry standard, so unless they're misconfigured one might guess at a design flaw or stability issues on the back end. I see the site is at 3.6.8: The 3.7 series has been out since around April, and is currently at 3.7.2PL2. In the dim and distant past, getting the database caching right was a bit of a black art, too. And addons could cause random conniptivity.
Ooh, just spotted this: "
vB 3.6.8 has known security issues so I *strongly* recommend that you upgrade to the latest version."