FYI, the problem is with the Recent Comments widget code that ships in the Wordpress base install. Page.ly had the same database connection dropping issues you did and I presume for the same reason. (edit: By the way, use the db-error.php facility to put up nicer error pages. It's also a really obvious point to insert some monitoring logic -- I think customers would like it if you noticed their problems before they do).
The core issue, as I said elsewhere in this thread, is that unless you partition the underlying wp_comment tables, performance becomes steadily worse as the total number of comments rises.
The only reason that this was never a problem for me on my own servers is that I am loltastically over-provisioned for my requirements. I just never saw it.
You will see it more in future. Like I said: this is not a badly behaved 3rd-party plugin. This is mainline code. Your customers can reasonably expect that you can run Wordpress out of the box without degradation.
None of changes the fact that my original migration experience was a total disaster. I know you're experiencing growing pains.
Well here's one of them. I hope it serves you and your future customers well.
Yet in my pinboard I have this bookmarked: http://pento.net/2011/04/28/partitioning-the-wordpress-comme...
Yup, I had to partition the comments table.
I've been watching this too: http://wordpress.org/extend/plugins/postgresql-for-wordpress...
I'm willing to accept fractionally slower page loads, as for the most part they're cached heavily post-generation. I'd feel far more comfortable partitioning in Postgres not least because I'm far more familiar with it.