Everything above sounds just fine to me. More than enough memory for pages that are taking ~10-12 MB to load, not too many queries, snappy load times.
I'd really talk to your hosting provider or IT support to see if you (or they) can look at the MySQL and Apache logs. If MySQL is disconnecting, there's something wrong which could either by a MySQL issue or an Apache issue (it's crashing part way through page load, preventing further database queries).
Unfortunately, there's not much more I can say from what you've posted above. Again, if you can easily recreate the issue, feel free to disable the JFBCSystem and JFBCContent plugins to see if the error goes away. If it does, we can definitely investigate it further (we'd need access to the site). This isn't an issue others are reporting, and we can't recreate it though, so there's not much more we can do under the current circumstances.
Best of luck to you, and definitely let us know what you find!