I have been suffering from a still unidentified bug in either my WordPress install or the server it runs on, or possibly somewhere the two intersect. After trying the basic first steps (turning off all the plugins to trouble shoot), and the more advanced diagnostic steps (stripping out as much content loaded from offsite as possible), I still don't know what is causing the issue. Media Temple's tech support is similarly baffled.
With all possible causes eliminated, I am going back through them again, only this time I am also replacing my blog theme. And so I have switched out the theme I have been using for the past several years with a basic free theme from WP, and I'm currently using it with as few plugins as possible. If the problem continues then I know for sure that the problem is the hosting company, and not me.
P.S. On the plus side, one side effect of this debacle is that my site will be about twice as fast as it was a couple weeks ago, and each page will be about a third of the size. That's how much detritus I have cleaned out from the blog.